Depends on availability but I would say the chance of receiving permanent housing from QR is 50/50.if they don't have anything available you are given several weeks in hotel and allowance to find your own place. If you do get housing it may not be a villa. I was given a 3 bedroom apartment although captains are supposed to get villa. After several months I was offered a 4 or 5 bedroom villa, but didn't want to leave where we are.
You may ask the recruiter, QR has villas at Ain Khalid Gate and Pink Villas, as well as other places but they seem to be more of a waiting list for better locations. Holiday Villa is only apartments but location is little better.
Most companies in Qr pay much more for housing allowance so prices are increasing. I am guessing 14000 is required for descent place.
Rumors have been floating around of an increase for captains up to 14000, but time will tell.
I haven't been to Al Wakra area south of the new airport but have heard it may be descent option, especially as new airport opens up.