Qatar Airways joined the Oneworld Alliance on October 30th, 2013 (read more here). Qatar and American Airlines started the partnership already a month earlier for earning award miles and using them for trips (read more here).
I took four Qatar Airways flights in the past week and can confirm that they are correctly posting to American Airlines AAdvantage program. I just had the above flights posted overnight.
Sometimes there are glitches with new partners, but seems that at least the Qatar Airways flights post just fine for AAdvantage program. Hopefully it works as smoothly for Qatar Airways Privilege Club members that collect miles on American Airlines flights.