I flew to SYD with BA and came back to SIN with QF, before my onward flight to LHR with BA, and they were very strict about my allowance on the QF being QF's allowance and not BA's. They even double checked if they could waive a bit of the fee as their top tier get a little bit of extra allowance, but they couldn't. So I think you'll be stuck with QF's allowance on their metal.

I was lucky as my QF flight was forced on me due to BA cancelling flights last year between SIN & SYD on certain dates. I got my excess charge back from BA, which was brilliant as QF's charges were high even on just the short hop up to SIN.