AA miles are worth a lot more than Qantas miles generally ; if booked on AA for the flights, then if in economy, if the booking class is eligable to accrue miles, there is a good chance that it will only accrue at 50% to Qantas

Credited to AA and will earn 100% so would earn 11,954 which is 546 miles short of a 1 way flight within north america. If credited to QF would likely earn 5977 miles . I would recommend crediting to AA. If you have plans to use AA in the future , I would also look at taking one of AA's challenges since with that trip you can definitely attain Gold status and possibly Platinum via the challenge