Hello,
There is a Doha Driving School in Khartiyat. This should be closer to you and they have a pic-up and drop facility. The charges are approx 90 Riyals per class and the full classess are for 30 days after which you give a test. Problem is you may have to wait for around 2 months only to get a car for driving class. Neways just check with them n u wld get all d details.

Cheers !!! adn safe driving.