If you speak Arabic well, you stand a better chance of landing a job in Qatar as compared to those non-Qatari fresh graduates who don't. You can try your luck for that very rare possibility. However as pointed out above, fresh recruitment are less in numbers and hence locals are preferred over anyone arriving from across seven seas. Don't want to discourage you but my suggestion will be to go ahead and add at least a couple of years as your post educational experience before taking a plunge. Companies here would look for results rather than allowing you time to gain experience.
Good Luck