Buy if you can buy....but presumably being new to Qatar you won't be in a position to buy so renting is the only way forward! I've done long term rents with Hertz, Eurodollar and now National who have been great. International brands aside, you can also use the local companies, though these can seem quite shady and unreliable at times! You're also likely to get an older car which smells of smoke...but you won't pay top whack for it. My advice, go for a recognized brand.
When you take in to consideration there's no maintenance or insurance payable, then it's not a terrible deal, plus if you have to leave on short notice (not unusual) then you have one less thing to worry about!