The only thing I was aware of was the ability to earn miles with some hotels. You may want to check the Orxy hotel as I believe QR owns it.

You really can't go wrong with selecting a hotel in QR as they are all 5* (same as QR)

I think the only things worth seeing in DOH;
Dune bashing (if you haven't done this before)
trip to the inland sea
the souq.

All can be organized with QR for day trips or you can find company's online as well.