I have no knowledge of the NZ market but unlike travel within Europe it has always seemed to me that it matters less when you book long-haul travel and most of my trips have been relatively late bookings. Even my fortnight in China last year I booked less than a month ahead for about £580 return which I considered quite reasonable. I’ve actually once booked, and seen a few times, extremely cheap last minute long haul flights.
I’d suspect if you travel non-stop next day it will be far from cheap but if you travel via somewhere it may be more reasonable than you think, excepting school holidays, Christmas etc. Why not do a dummy booking?