Unfortunately, apart from a brief period earlier in the year, CX flights do not show on the QF website when searching for awards (many believe they ought to, and I think once upon a time they did (?), and they may even do so again, but just not now).

You'll need to ring QF to assist with finding availability. Seems to cost whatever the QF flight costs +5K points (eg. MEL-HKG on QF in J = 60K points, on CX in J = 65K points), and they'll also hit you for the 2.5K points assisted booking fee. You may be able to talk your way out of that, given there is no online option to make the booking, but I don't think people have had much success trying to do so in the past.