captjns, if you go to the Qantas website and attempt a booking just on that JFK-LAX or LAX-JFK leg, Qantas will not sell you a ticket. If you came from one of their Australia flights into LAX, it would be fine to connect to it, but they can't handle USA origin/destination traffic. Also, reading ZED fare agreements for US carriers, they expressly prohibit you to ZED-nonrev on this leg as well.

Iceman49, that flight that jns picked is a QF flight on QF metal, not one of the AA codeshares.