Yes. Book everything using your AA FF #. Then on the segment you wish to accrue QF miles, ask in the Admirals Club or at Check-in to change your FF number to your QF card before you fly.

I do this all the time with CX and it works a treat.

You must do this before you fly on the sector (you can't simply send the boarding pass with the AA FF # to QF, they'll respond saying 'Already credited to another programme' regardless of whether it was a qualifying fare bucket).