You can try looking on the Qantas website (there is no U in Qantas!!!!) for availability. You have to sign up for an account, but you don't need miles to search, I think. Not necessarily the same as AA availability but if you see it in both places at least you could be pretty confident it is real.
Right now I see PE availability on QF74 SFO-SYD on 30 Jun, QF56 LAX-BNE on 1 Jul & 3 Jul. No J availability.
Other options with AA miles in J could be found on HA (through HNL) or FJ (Through NAN). Not as good a J product but still better than PE.