We've done NZ with DD twice - once when she was about 5 months old, then in September this year, when she was 3. We generally go Qantas, because we're almost always stopping in Sydney too. OH is a Kiwi/Aussie hybrid. We didn't break the flights with stopovers this time, as we were very time limited, and to be honest, either way is grim. It's a day and a half travelling no matter which way you go, and to be honest, we just thought we'd suck it up. We're coming from Scotland, so it's 4 flights, which ever way we look at it.
DD was surprisingly good - we took her to a quiet bit of Bangkok airport on the way out, and let her run about as much as possible, which helped. She was out of sorts, but to be fair, so were we. We did have a seat for her this time, which really helped, as it meant we had the 3 together by the window, and could squirm/swap around as needed to.
Flights generally come out a year before (well 364 days) and I'd say that's often a good time to get a decent deal. If not, watch for the airline sales - we have had decent discounts in the past. We've used FlightCentre before, who are quite good, we've found. Also, we have frequent flyer cards with Qantas, and you can save up points for internal flights/car hire/etc.
You will have an amazing time, I'm sure! I could bore on for hours with our advice, but I won't here. If you think there's anything I can help with, please do feel free to PM me....
Enjoy!