In September I succeeded in booking a business class award on AA.com for a QF flight in Australia. I wasn't able to complete the transaction online, though, so wound up calling the reservations line and getting transferred to an award agent, and the agent was able to book it. So perhaps try that if you haven't already.
In the meantime, I have another business rewards story that happened just yesterday. Expert Flyer was showing 3 business reward seats available on a different QF flight within Australia. I looked tried looking the flight up on up on AA.com but only economy rewards were available. I then tried Alaska Air -- ditto. In a desperation move, I finally looked it up on British Airways, and there they were -- 3 business class reward seats, and half the points that Qantas wanted on its own website. I transferred some American Express points to BA and was able to get the two tickets I needed.
Wishing you luck!!