Welcome to Flyer Talk FlyingKangaroo

Be aware that the cheapest economy fares on NZ are non mileage earning. Do you have the fare name or booking class so that we can check that?

While all Qantas fares are mileage earning on the Qantas program, some red e-deals are not mileage earning when credited to other airlines - eg American Airlines (again fare class will help determine if this is the case for you). For someone based in Australia and not an overly frequent flyer, the Qantas program will probably be best since you can easily earn miles through credit card and other local spend.

Air NZ's frequent flyer program, Airpoints, usually requires a $50 (AU or NZ) joining fee. So unless you will be flying a lot on Air NZ I would not recommend joining it, instead choose United Mileage Plus (awards are relatively cheap even though they just increased miles needed to/from australia, and no joining fee).

Enjoy your trip