I am no expert but I think if the codeshare is available you should be able to book through that, unless Qantas has a specific policy or the person you are booking through doesn't understand why you would want to do this. Maybe this is one of those times when it's best to use a travel agent.

If you are doing it purely for fuel levy savings and not frequent flier miles then I don't think using a different codeshare will make a difference because you are booking a qantas flight through qantas. I know AA doesn't pass on all fuel levys for other airlines however I assume Qantas does incorporate all fuel levies, that's why I booked my round the world through AA.