I managed to snag CPH-DOH-MEL for mid-April in J through Velocity, and there was heaps of other availability too on QR (including on the way over to FCO at the start of school holidays, although I booked that leg on EK F through QF, astronomical carrier charges and all). The same itineraries were available on AA, AS and BA. So yes, QR's providing plenty of availability.
Of course, for QF, there's nothing on QR.
(A tip if booking QR through VA is to look sector by sector. I'd initially booked CPH-DOH-ADL-MEL, online but noticed a quirk of the booking engine on VA in that it didn't show a complete itinerary for CPH-DOH-MEL for the Europe-DOH and DOH-Oz legs, either because the layover was too long (9 hours) or the sectors were on different days (not sure which). Calling in, they were able to book it for me - and I didn't have to spend half an hour on hold either, unlike the usual experience when calling Qantas! (There was plenty of SQ availability too).