That is a common connection to make - you should be fine. If BA is late then you'll get put on the next QF SYD-AKL flight (a few hours later).

Assuming your checked baggage is tagged all the way through to AKL, all you need to do is head for international transit, go through security and take the lift up 2 levels to the F lounge. You can get your QF BP inside (if you haven't already gotten it) - but will likely need to show your BA Gold card to get into the lounge without the BP.

Then relax in the very nice SYD F lounge for your flight to be called. You may want assistance or leave the lounge a bit early as the calls can sometimes be rather late (and more than once my flight has not been called at all ).