Suck and chew
Nothing grates more than a parent who is doing nothing to stop a crying child when the crying is avoidable. Now is not the time to use your parental tune-out tricks. Little ears can hurt with altitude and it's only fair on kids and others that parents are forearmed. We always travelled with a dummy, then a silicon toothbrush for our daughter to chew, stimulating her swallow reflex and helping her ears.
Walk it out
I see parents trying to corral their children around their seat, but if they want to stretch their legs, let them walk the aisles. Follow them, nodding to fellow passengers as they smile at your clean child. Remember, they can't go far.
Sleep
Other than babies, young children will likely not sleep on a transtasman flight. On long hauls it's easy - with departures timed for sleep, cabin lights dimmed, and other passengers asleep, it's inevitable. It was a rude awakening when we flew from Auckland to Fiji and our daughter was wired. Be prepared for this and accept their sleep routine may go west. Upon arrival try and get on your regular routine as quickly as possible while being gentle with your expectations.
When in doubt ...
Get your boob out. I was a champion extended breast feeder and made sure that when we flew the first couple of years I wore a top that meant I could resort to the boob if required. I was prepared to try anything to keep the peace on a plane and my face dared anyone to cross me.
Ditch your handbag
Backpacks are made for travel with kids. A backpack leaves two hands free, which will be absolutely necessary to hold soft toys, children's hands and all the other accoutrements thrown your way. Pack your handbag for later.
Think about the toys
My daughter's two favourite travel toys were small containers of dried macaroni and colourful pom poms. Those two travelled with us for years, were small, engaging, cheap and replaceable, but are not appropriate for a plane. Trust me, you don't want to be taking toys on the plane with lots of little parts that can easily roll off a (disinfected please) tray and hide under seats and feet. Good luck scrambling around to collect all the pieces.
Get your head in the game
I maintain that travel with kids doesn't need to be a big deal but in case you are still worried, do what I did and mentally prepare yourself for the absolute worst; screaming, no sleep, crying, vomiting. Anything above that will be a success. Bon voyage!