You either collect to AA or collect to QF ; you cannot do both
You will likely be much better off crediting to AA and ideally book on the AA codeshare
LAX-SYD r/t can earn 29.,952 miles to AA ( esp if on the codeshare) . Consider that 125,000 is enough for a business class return - so 4.2 r/ts will get a business class return
Crediting without status to Qantas would earn 14,796. The cost to upgrade r/t from economy to business would be 144,000 points return. 9.73 r/s will earn enough for an upgrade to business from economy
I would suggest forgetting about upgrades using Qantas points and just redeem for free business class travel ( plus taxes )