Sounds like a not bad deal. With housing costs covered off, you're only responsible for food, transport, entertainment/travel and savings. If you rent a car, look at spending 1800-1900 QR/month, so buying is definitely a good option. I got a 4-cyl SUV used for about 25000 QR (about 40% of new) and I'm pretty happy with it. I know people who rely on chauffeur services at about 50 QR round trip so they don't need a car (but they do need to plan all their outings to the 5 minutes), so car/no-car is a personal option. I would agree with TJ not to rely on public transport--it frankly sucks here. Food is pretty cheap for one person (maybe 300-600 month depending on personal preferences--food from home always costs more).

Housing construction is basically cindercrete and concrete so houses have a great deal of thermal mass, meaning they retain daytime heat through the night and take some time to warm up in the daytime. So even if temps drop to 5C overnight, the house takes longer to cool down (unless daytime temps don't get much above 15C like they did in January). I found a sweater/fleece by day, and a quilt by night was enough to keep me warm. I know some that did invest in electric heaters for their living rooms.

Hope this helps. Welcome to the Gulf! (I say this while I'm on leave in cloudy western Canada where it's only 20C today)