This is an excellent idea. As PHL stated, the reward inventory is NOT exactly the same, but pretty close - and the best place to start.

I've done the reward with US in First and CO in Business.

QF does generally open up more reward seats within 2 weeks of travel, but that is a role of the dice you are making if you don't already have something else confirmed.

Also note that for Biz availability, you can check LAX-SYD, LAX-MEL, LAX-AKL, and LAX-BNE.

Note that even though BNE (Brisbane) is via AKL (Auckland), award inventory is NOT the same. I was on a F award about 18 months ago that was available LAX-BNE that was NOT available for just the LAX-AKL portion. That was, of course, when LAX-AKL had First Class.

And remember you are allowed to cross the Tasman Sea (that's the water between OZ and NZ) ONCE but not twice, so if you fly to AKL, you can then fly across to Oz on the reward ticket, and then leave back to LAX from Oz.

For example, LAX-AKL-SYD-LAX is OK. BUT LAX-AKL-SYD-AKL-LAX is NOT OK.

Happy travels and good luck.