Up until about 3 months ago it was fairly easy to book a LHR-AKL with QR... unfortunately every man and his blog has waxed lyrical about how just 90k avios will get down under on QR and its seems QR availalbity has all but dried up, unless youre will to pay the double avios to unlock more seats.

In short you cant be too fussy about exact dates, or even carriers... book the outbound as soon as you can, and with BA you can ring up and add the inbound once it becomes available.. with QR i usually just keep the outbound/inbound as sperate tickets..

Also if you do fly BA there is a the option to use avios on QF, and they even have some widebody planes from SYD-AKL too (1 or 2 a day i think).