Qanat Quartier - beware
Some much better rental prices at Qanat but (this is second hand info) there are quite a few problems in this development. People have been leaving due to noise (watercraft in the canals), build quality (mold, leaking pipes. electrical problems) and odour. There are no facilities and at the moment, no safe way to cross the road to Porto Arabia or Medina Centrale.
Goat: Empathise with your position as I started in exactly the same fix. Company accommodation promised, but on arrival given a very short stay in a hotel then out on the street. We stayed in temporary quarters and eventually found satisfactory accommodation, but it was not a villa. We purchased furniture, we pay utilities, AND the rent (until recently) was more than our allowance. The compromise is satisfactory as we live here so made this a home rather than a "place to stay".
Finding a place to stay in Doha is not a problem. The problem is finding a satisfactory place to live while remaining close to the allowance. Single people have a lot of "sharing" opportunities at a furnished/serviced apartment that will remain within the budget. Couples and families have more of a challenge but it is manageable. Take your time to look around once you are here and have secured information and transportation, preferably with your partner. Location, facilities, price, and budget must be placed in priority depending on your circumstances.
Expect no assistance from Qatar Airways in this endeavour other than some suggestions for temporary quarters. If they DO present you with company quarters, grab it. This will present the best opportunity to settle in and explore other options OR, stay where you are.