I believe that if they are both PNRs ticketed by QR with QR flight numbers, you shouldn't have an issue. Unlike other OW-members (pointing fingers at BA!), they should be able to check your luggage through.

I think they will need to link your PNRs together, this can probably be done at check-in and they should be able to issue you boarding passes for both flights. Just make sure you have all the documentation ready. You just won't be protected should anything go wrong.

There is an extensive thread on the subject: Transiting through Doha on Separate Tickets