So long as DOH-AKL is a route they will fly, the B777-8X is a plane they will need, as that requires at least 3 frames all by itself. In fact, until SQ resumed Flights 22 and 21, that was the world's longest flight, blocked at 18:20 on the return.
I believe DOH-AKL-DOH to be perfectly doable with the A35K - especially at 319t.
From the QF Project Sunrise thread, member flipdewaf
(Fred) has run some numbers which show that the A35K can do some amazing things (I'm not discounting the abilities of the 778 but with that one being a thoroughbred ULR bird, its capabilities are expected).
Now, I realise that Doha is HOT, but QR920 (DOH-AKL) departs at around 0200am and is the shorter of the two legs (AKL-DOH being longer, time-wise) so performance should not be compromised.
Never be proud. Always be grateful.