American Airlines and Qatar Airways frequent flier partnership has commenced today (September 23).
Both American Airlines and Qatar Airways frequent fliers can now earn and redeem miles on each others flights.
The earning of elite qualifying miles will likely not start before Qatar Airways joins Oneworld alliance on October 30, 2013.
Qatar Airways has published a list of eligible AA fare classes for Qmiles:
You can access Qatar Airways web page for American Airlines partnership here.
American Airlines AAdvantage eligible Qatar Airway fare classes:
You can access American Airlines web page for Qatar Airways here.
We should learn later today the eligible fare classes for American Airlines mileage accrual on Qatar Airways flights. I will update this piece at that time. Edit: Now updated with the American Airlines Qatar earning chart as well.