Update on the monthly rent, you can find a bedroom at Ezdan tower Westbay for QR4500. This includes:
1 bedroom and a bathroom
2 days a week room cleaning - free of charge
Internet & electricity included
State of the art GYM - free of charge
Olympic size POOL - free of charge
Covered parking
Fully furnished - Centrally air conditioned, LCD TV, table, chairs, fridge, cupboards, etc.
(http://www.qatarliving.com/node/3471211)

Open a bank account, and transfer your salary there ASAP, and get a car loan. With around QR1800/mo for 4 years, and the car is yours. Or save up for a few months, and buy a cheap (used/new) compact car for QR15K-QR50K in cash. Check QatarLiving classifieds for prices.

QNB, Doha Bank, CBQ are the top 3 banks in Qatar.

I think QR10K should cover your basic needs including phone bills (use Skype for international calls), car+gas, food, and social life.