Yes you could get a 1 bedroom apartment for much lesser than 8K/ month and use the rest on the car, but 1 bedroom apartments are not easy to come by. Also, buy a car rather than lease one. You don't have to make down payments on cars no more. 

Cost of living depends on your lifestyle, but I'd think about QAR 1500-2000 on your groceries and then approx QAR 150-200 on dining out at a decent resto once a week.

If you're into drinking/ clubbing, a LOT more will be spent ;-)