Just go to
www.qantas.com.au (for SYD-CHC),
www.qantas.co.nz (for CHC-AKL) and select flights. Sounds like you want the cheapest category.
If you dont like the fares now there is plenty of time for specials to come along (check the QF forum and/or qantas website regularly). The dates of travel are outside NZ school holidays (not sure about australia) so there should be specials at some stage (too early now).
You can get e-tickets for these flights so no need for australian address.