With American Airlines, A class can have interesting results when crediting to Qantas frequent flyer; mainly due to it being used both for revenue (discount First) bookings and SWU/miles upgrades.
With the former it should credit as First; with the latter crediting should be as per the original fare class booked.
I have flown in A class in both of these situations and crediting has required close watching as there is little consistency with how such travel may credit.