You typically wouldn’t be able to upgrade a Qantas-issued ticket for Qatar points, and vice versa (in general, but I’d be very surprised if QR/QF were different in that regard). Only Qantas would be able to help you, and as you said, you’d have to pay the F price then.
Your only chance would likely be a cash upgrade at the airport.
Or trying to convince Qantas that they shouldn’t charge you for F.