SYD is refreshingly straightforward to transit in. You'll technically have to enter Australia as you're having to check in for a separate flight (as though you'd arrived from outside the airport to check in for it) but it's a lot less hassle compared with doing the same at LHR / anywhere in US etc. In my experience BA15 is usually early and circles offshore before landing right on the curfew time at SYD, and the last time I went through we were literally the first people of the day at customs etc.

Be sure to hold on to your BA First boarding passes to ensure you get into the wonderful Qantas First lounge while awaiting your flight to NZ

Happy travels!