The family is blissfully unaware that their species is under threat.
Throughout Africa every year, 30,000 of their kin are poached to support the huge world market for exquisite ivory collectables, mainly crafted in China. Despite import bans, the trade in inflation-proof, "white-gold" ivory products is booming and scientists say the future of these regal giants is in doubt.
As we bounce along the rough bush track between sweet thorn thickets, succulent bushes and the euphorbias that comprise the Eastern Cape's spekboomveld, I reflect sadly on the state of Africa's wildlife.
But more is to come. We pull up beside a rhino dung heap midden and Vorster describes it as the rhinos' current "Facebook Status".
The herd's home range is scent-posted by dung heaps as marker points to define their territory.
Nearby, a group of massive white rhinos grazes peacefully. The grey, dust-covered herbivores are so still they look like giant ridged boulders, completely immobile except for their twitching ears.
Not being under constant threat of predation, they seem like private, docile creatures browsing happily in their own little world. Looks can be deceiving, as the 2½ tonne beasts can run at 40km/h in short bursts and use their metre-long first horn to devastating effect.
But the rhino's horn is his Achilles heel. It merely comprises keratin, calcium and potassium, the materials that make up human fingernails and hair.
However, the Chinese still attribute it with medicinal properties and crave it as an aphrodisiac. The Vietnamese have come to value the horn powder as the party drug of choice.
So, on my first African adventure, I'm shocked to the core to learn that, worldwide, white rhino numbers have declined by 90 per cent in the past 50 years and ecologists warn they may become extinct by 2020.
In the meantime the animals have to be monitored day and night by armed military specialists to protect them from poachers.
The large herbivores - elephant, rhino and buffalo - have earned their place among the Big Five that trophy-hunters of an earlier era regarded as the most-dangerous to stalk.
The other two - lion and leopard - are also subject to illegal hunting but on a lesser scale.
African lions have lost 80 per cent of their geographic range over the past century but are largely protected from the "great white hunters" of yesteryear.
When our game drive comes up to a pride of lionesses, sub-adult males and one lion with a straggly tawny mane and pale yellow eyes, my heartbeat rises rapidly.
This pride must have had a right royal feast last night as they are sprawled out in a languorous state with bloated stomachs and hind legs raised in the air.
The matriarchal lioness sniffs the air and rolls on her back in a somnolent daze and the lion gives a deep, guttural roar and settles back to sleep. The pride of Africa lies blissfully at peace with the world.
Finding the elusive leopard is our guide's biggest challenge. Even with a radio tracking device we need to traverse vast open savannah and riverina regions to find one female loping along a dusty trail, dragging an impala carcass.
She stops under a shady marula tree and devours her prey, completely disinterested in the human onlookers.
These beautiful yet secretive animals with their striking spotted coats are classified as Near-Threatened because of habitat loss, conflict with farmers, hunting and the fur trade. Technology is playing a part in South Africa using facial-recognition software to identify leopards from photo records on a database.
There's also a project to register all the country's rhinos on a DNA database from tail hair and blood sampling. The DNA profiling will link anyone with illegal possession of horn to a rhino that has been found dead in the bushveld.
My final wildlife sighting of the day is my favourite, which fortunately has no sombre overtones of exploitation.
A journey of giraffes crosses a rise in front of our vehicle, silhouetted against a clear blue sky.
The amazingly regal creatures are the height of elegance. They demonstrate their fantastical, slow gait as they approach and peer down on us with dark liquid eyes from five metres above the ground.
I can see why visitors love the world's tallest animal, which comes high on
"must-see" bucket lists after lions and leopards.
Giraffes are the most-photographed animals in the game reserves. Their cute new-born babies are taller than most humans and are able to run after 10 hours.
The patchwork of brown and yellow camouflage spots on their hides is startlingly beautiful in the sunlight, glowing like a 3D image.
What also amazes me is how much time they can stand still, staring blankly into space as if any form of action is simply too much for them to contemplate.
Maybe they have a wicked sense of humour and think, "I wonder how long I can out-stare these puny bi-pedal mammals?"
Back in the comforts of Shamwari's Long Lee Manor, I shake off the dust of the bushveld, sip pre-dinner drinks and think of Africa, the crucible of human civilisation and a country to be treasured for its unspoiled, untamed natural beauty.
Then I think of the disconnection between the glorious wildlife I have seen on this responsible safari and the heartless destruction of mega-fauna for financial gain.
The message for Asia is clear: there's nothing curative or libido-enhancing about fingernails, hair or rhino horn. Africa's wildlife is sacrosanct and must be preserved at all costs.
Fact file
Getting There
Singapore Airlines flies from Auckland to Cape Town via Changi Airport, Singapore.
Getting Around
Adventure World organises small group tours around South Africa in modern vehicles with local guides at each city to show you the sightseeing highlights. Carry a supply of lower denomination currency as tipping is common in South Africa.
Shamwari Game Reserve
The 25,000ha, malaria-free reserve in South Africa's Eastern Cape, on the popular Garden Route from Cape Town to Port Elizabeth, has seven luxury lodges in idyllic settings, including a remote tented camp and a family-friendly lodge.
Paul Rush travelled to South Africa with assistance from Singapore Airlines, Adventure World and Harvey World Travel.
