Yes, you should be able to do this. Since your AONE3 is an international ticket, you cna be booked on the QF 107, even if you are not flying QF on an international segment. That said, there have been instances of QF denying boarding to people not continuing to/from Australia/New Zealand.

In your case, I would go for it. The worst case scenario is that QF decides to deny you boarding at LAX, in which case you can still avail yourself of the numerous AA flights to JFK, which offer, IMO, a very high standard of service.