I shoot abroad quite a lot. I stick all the extra bits and bobs (chargers etc) into hold luggage. I then wear something that has pockets, big pockets, so I can put small lenses into them (eg 50mm) and my hard disk drive and card reader. And then I can just get the rest of my pro kit (2 bodies one with battery grip, 70-200, 24-70, 85, and sometimes 100mm, plus flash) into a bag with my laptop. It's so close to the baggage limit for Ryanair, but it's fine for most other airlines, so I'm guessing you'd have more capacity for NZ. But the main thing to watch out for is the bulkiness of the bag as they will make you put it into the hold if your bag won't fit the thing they test bags in.
By the way, I do know plenty of photographers who successfully put their pro kit into the hold using things like the Peli.