Don’t forget AS also for SCs and points.
You can book QF codeshares on QANTAS.com but only in conjunction with long haul flights in/out of the US. Can be reasonable value (and provides protection if flying onwards from say LAX/SFO/DFW same day).
If you just want standalone internal flights book direct on AS or AA.com (US website). Booking AS is pretty straight forward and I’m finding them cheaper than Aa for domestic First. The AA website will try and take you to the Oz website - and potentially charge you more.
Note that both AS and AA “First” on two class domestic planes earn “Business” SCs (if you’re using the QF calculator).
ITA Matrix is handy for finding cheap‘ish routes.