The OW Explorer tool doesn't allow you to pick and choose, you have to pick the class for the entire itinerary. However in the itinerary I did is also included LAX-JFK on AA metal: this flight is on a A320/321, which is coded F. OW had no problem with this as far as AA is concerned, but the situation with QR J flights being coded F is identical.

I will try doing the entire itinerary in Y, just to see whether QR is still left out of the calculation.

EDIT: yes, the same problem occurs even in Y. Only RJ flights to DOH, via AMM. And I have tried on different dates.

It seems strange to me that OW would leave out QR on their RTW routes. I can book a return CAI-DOH through the OW website, and that does allow a direct QR flight.