AA uses SABRE for its reservations system - if booked with AA, generally the only way anything will show up in 'your booking' with Qantas.com is if there is a segment in the booking with an airline that uses the same booking system as Qantas (which is Amadeus).
Even, then, often all that will show is specific flight(s) and related transfers. Other flights on carriers that do not use Amadeus might not show.
An AA booking with a BA flight segment but no QF segments and having your Qantas Frequent flyer number in the booking may show on Qantas.con since BA use Amadeus.