It is illegal for unmarried couples to co-habit even in hotels. If you were both white European/Westerners, you probably wouldn't be asked.

However, your GF is from Asia and she will attract attention simply because a large number of prostitutes in Qatar are of that ethnicity. There is no guarantee you'd be prevented from staying but there's no guarantee you won't

Hotels do keep track of who is checking in with who and may even question ladies who are going up to rooms. I have experienced this myself in a 5* hotel where the hotel had a staff member stationed at the elevators.

Might you get away with it? Possibly.