JNB-DOH and DOH-ORD are both operated by QR. AA just happens to be the ticketing carrier for the second flight (because it is an award ticket).

It was my understanding that QR will through-check baggage on separate oneworld PNRs as long as MCT is met (which it is — they are selling this connection, and I imagine a number of people are making the same connection (as the US Embassy is advertising the flight).

Calling the local QR office is good advice.