As long as on one ticket and your bags are checked through you should be fine. On arrival go through international transfer security (before you reach immigration), then up to departures level. If you haven't already got a QF-issued boarding pass head to transfer desk to get one (can do this in the lounge also). Transfer desk is behind you when you reach departure level from transfers. You should have just enough time for a quick bubbly in the F lounge (take the lift right where you come out from transfers and up one level - F lounge is on the right behind glass door with a bouncer out the front) before boarding.

If your BA flight is late you'll need to go on a later flight, but QF have plenty so that shouldn't be a problem.