There is no oneworld option from North America to NZ direct.
Main options are QF direct from LAX/DFW/JFK (via LAX) to SYD/MEL/BNE
CX via HKG
JL via Tokyo
LAN from South America
What class are you planning to fly? QF transpac awards in premium cabins are probably as difficult to find as BA LAX/SYD flights.
QF releases awards up to 355 days in advance, and I think CX/JL do as well.