I've just got a job there & I'm Australian (coming from Bahrain - don't know if that makes a difference). My visa took about 2 weeks.
However - I had to wait about 3 months before my employers made the decision. I have heard that quick decision making is not a Qatari virtue.
My feedback for what its worth is that visas for Pakistanis and Indians are difficult to get because their quotas are near full but that for westerners its comparatively easy.