Other dolphins occasionally swim upriver to visit but guide Phil Doddridge identifies the locals by their fin shapes and scars. Twinkle, for instance, has tell-tale markings from his multiple run-ins with fishing lines and rope.
Phil has been kayaking round this area for about 20 years so he can also identify the species of tiny fish that leap out of the water, in glittering tandem, on this warm, serenely still day. He also names the birds and stingrays that flap ahead of us en route to the ship's graveyard.
Phil's two-hour tour leads the four of us - Tom and I in one kayak, husband Marty and 10-year-old Jake in another - away from smoke stacks, amongst mangroves and right up against the rusted hulk of a historic iron-hulled ship.
The Santiago was built in Glasgow in the 1840s and is amongst at least 30 vessels that were deemed useless and scuttled in the port area. These days, the remains are considered archaeological treasures.
In nearby Port Adelaide, the beautifully laid-out South Australian Maritime Museum offers engaging stories about both the ships and the dolphins. The port town itself is awash with grand, 150-year-old brick cargo sheds and warehouses and half-a-dozen museums. Up the street from the seahorse farm, the maritime museum is an instant, hands-on hit.
"Look, Dad. A ship. And you can actually climb on it."
Standing on board the ketch, the boys watch a visiting school group raise and lower the sails and load a bag of wheat onto the ship. A retired wharfie and an ex-Navy bloke are volunteer helpers, bellowing instructions and encouragement.
One even breaks into "yo ho heave ho" song. Our boys are particularly fascinated to learn, since there is no toilet on board, the captain and his cabin boys had to slide along a plank and drop their pants over the ocean.
We parents are especially enamoured with the grand figurehead collection.
Downstairs, visitors can climb into cramped cabin beds and view photographs of life onboard for the migrants who arrived here by ship.
By now, the boys are over the shock of being transported to Australia without warning. Travelling to Adelaide was an eleventh-hour decision, made possible by work commitments, understanding school teachers, air points and a "kids fly free" airline deal. With a lot of parental conniving and truth-stretching, our children had no idea they were flying anywhere until they found themselves standing inside Auckland Airport, bleary-eyed and surrounded by bags, at 6.30am on a Wednesday.
Big brother was instantly in raptures. His cautious sibling needed more convincing. Wouldn't there be sharks, he wanted to know. And what about the bush fires?
Tom is enormously relieved to hear Adelaide sits in the bottom left corner of Australia, thousands of kilometres from bush fire country. And he quickly forgets about underwater predators in the face of 30 degrees C heat and a string of wide, empty, white-sand beaches.
The gulf-protected waters are calm, clear and warmer than we are accustomed to and less than 20 minutes from the city centre.
Everything seems to be close in Adelaide, population 1.1 million, largely thanks to early city planners who surrounded the downtown core with massive tracts of parkland.
This has naturally compressed sprawl, ensuring the lovely old university, a string of impressive museums and galleries and the zoo are all within walking distance of the main shopping street. Traffic flows easily through and around Adelaide and, on a good day, the airport is 10 minutes drive from town. A couple of hundred winery cellar doors lie within 90 minutes drive, too.
In the city, we walk almost everywhere, collecting gum nuts and answering questions about killer crocodiles en route. When small legs become weary, we hop on one of the free bus and tram services that service the central city. This is a superbly easy place to travel with children.
And it's a fitting sister city to Christchurch. Aside from the fact that Edward Gibbon Wakefield had a hand in planning both cities, there's the shared flat terrain, parched summers, the historic stone buildings, the focus on art and culture.
The fringe festival is unfolding during our stay, which explains the man squeezed hotly into a tall, white, space shuttle suit, shuffling stiffly along the street to hand out brochures.
Inside Adelaide Zoo, we quickly find the essential kangaroos and a single, fat koala dozing in a tree. There's also a sloth, behaving in a predictably sloth-like manner, but some of the other nocturnal critters are great fun, like the meercats that don't seem to know they should be asleep. I'm particularly enamoured with the Dunnart, a crazy little native Australian mouse-like critter with road-runner speedster tendencies. It reminds me of a wind-up toy.
In the heat of a drought-stricken city in the driest state on the world's driest continent, we gulp water and dart gratefully between the zoo's generously scattered shade trees. We are awed by the size of the fangs on a Tasmanian Devil and by the lurid plumage and human-killing abilities of a cassowary bird. It makes our native birds look pretty wimpy.
We strike the pelican enclosure at feeding time and meet one of the mesmerising birds who starred in the 1970s award-winning Australian movie Storm Boy. I'm sure that movie made me cry and make a mental note to buy the novel for my eldest son.
The wilting children revive miraculously with a few more gallons of water, an icecream and the comparatively dark and air- conditioned quiet of the state museum.
They are loathe to leave the top floor of the museum, with its extensive collection of vicious aboriginal weapons and tools and a fuzzy movie clip of a scantily clad man using a sort of hatchet to carve a boomerang from a tree branch. It is a child-friendly museum, with interactive computer screens and plenty to poke and touch.
On the southern side of the city, at Adelaide Showgrounds Farmers' Market, it's not so much hands-on action as a multi-sensory assault of sizzling grills and buskers, colourful produce, wonderful tastes and a busker belting out Crowded House tunes.
The Sunday morning farmer's market is remarkably child-focussed, with its weekly kids club programme and supervised outdoor children's area stocked with stilts and Frisbees. Our boys don keepsake paper chef's hats and follow a mob of chattering youngsters into the garden to pick basil and zucchini.
Back in the designated kitchen, they grill the zucchini and make pesto from scratch, then assemble a glorious antipasti platter using local olives and other fresh, seasonal produce available at the market itself. They lurk around the neighbouring demonstration kitchen, gobbling generous samples, and happily cruise the 80-odd stalls for Italian pastries and organic apples, fresh figs, salami and strips of fruit leather.
South Australia takes its food seriously. Apparently, Adelaide boasts 700 restaurants and we can't get enough of the locally-grown olives and olive oil, almonds, figs and pistachios. The state's migrant history - we learn more at the Migration Museum - translates into wonderful Greek and Italian restaurants, Asian vegetable stands at the market, good sushi and Thai takeaway menus that feature crocodile meat curries.
But ask the 6-year-old for the high point in his trip and he'll shamelessly promote that most clichéd of Australian tourist activities; cuddling a kangaroo. For him, there is real magic in wrapping his arms around an animal that belongs in picture books at home. Most of the kangaroos at Warrawong Wildlife Sanctuary, half an hour north of Adelaide, are rescued orphans who bound up to our scientist guide in search of food.
We four foreigners are the only takers for tonight's hour-long dusk "family feed tour" of the sanctuary, where food is laid out for the predominantly-nocturnal sanctuary inhabitants. We hear black cockatoos shrieking overhead and spot a sole platypus, plenty of tortoises and several fat potoroos.
Dr Stephen points out the kangaroo berry leaf, which is used as a contraceptive, and tells us Australians are lousy at protecting their critters; every Australian native animal shorter than Tom is endangered.
But our youngest son has eyes for only one creature and spends his remaining nights in South Australia clutching a cheap, brown, stuffed toy, with a joey in its pocket.
CHECKLIST
Getting there: Air New Zealand flies direct from Auckland and departs and returns at civil times, in an Airbus with personal monitors/games. It's an easy flight of about four hours.
Where to stay: We can recommend the lovely old Medina Grand Adelaide Treasury for its spacious apartment-style rooms, great location and service and respect for history, including a mini museum in the foyer.
What to do:
Adventure Kayaks
South Australia Maritime Museum
Adelaide Zoo
Where to eat: It's tough to find good Greek food in New Zealand and Eros Ouzeri is good, located at 277 Rundle St.
Near Semaphore Beach is Sarah's Sisters & Future Cafe, 117 Semaphore Rd, ph (08) 8341
2103. It's a low-key cafe backing on to a garden centre, with imaginative, delicious vegetarian food.
Russell's Pizza is a hard-case pizza joint that's well worth the drive to pretty, historic Willunga village, 45 minutes south of Adelaide. Run largely by teenagers making stunning wood-fired pizza. Hours are limited and bookings essential. 13 High St Willunga, ph (08) 8556 2571.
Free kid stuff: Gorge on the sights, smells and fabulous tastes at Adelaide Central Market.
Visit Warrawong Wildlife Sanctuary during the day and entry is free. Animal shows and guided tours incur a charge and there's also the option of staying overnight in the sanctuary. There is no charge for the kids' cooking classes or supervised outdoor activities at Adelaide Showgrounds Market. Just register on the day, at 10am.
Entry is free at the state's impressive library, art gallery and museum and all three are lined up on the lovely North Terrace, in the middle of the city. The Migration Museum is tucked around the corner, on 82 Kintore Ave.
Look out for a copy of Adelaide Child, a free magazine that includes excellent, up-to-date listings on kid-friendly events, facilities and workshops around the city. See webchild.com.au for more details.
Explore by pedal with Adelaide City Council's "free bikes" programme. Borrow bikes, helmets and locks for use throughout the city - just hand over a drivers licence or passport at one of four city locations. Available 7 days.
Further information: See southaustralia.com.
