I have a rookie question...

I'm trying to book an F/J award on AA miles to Australia. Ideally I'd like to be on the A380 out of LA on Qantas, but I know that can be hard to find and haven't had any luck yet. (Looking to travel in October/November for 2 pax with very flexible dates).
I've been using the QF website to check for availability, and don't see much.
But, I'm flying out of NY anyway, so if I change and make that the origin some CX availability shows up. My question is, if there is availability shown on the QF award site does that mean that AA 100% has access to those seats too, or are there any seats that are designated for QF but AA can't book?