You may also want to check whether SYD-ZQN is operational. I understand it's seasonal (for the ski season). I don't know when you'll make it down here during your trip, but since Sept is beginning of the end of the ski season, it may not be working then.

If the flight isn't operational, you can try SYD-CHC then make your own way to Queenstown. Domestic flights are cheap, you can then fly or drive for CHC-ZQN then fly from ZQN-AKL to resume your trip.