Based on playing around in the QR app just now, it seems like (for me at least, YMMV):
If you search for MEL/SYD-DOH award space, you get the VA-prime flights as well as QR-prime.
But if you search for MEL/SYD-FCO/CDG, you get only the QR-prime departures from Aust.
So maybe it just won't...