Hi,
2 places which I know off are...
1. The CHN Institute - Not sure about the courses, but i think they have some crash course or something.
2. FANAR - The spiral mosque in Doha. The course they offer is in 4 Levels. Each level is a duration of 2 and 1/2 months. I have been attending level 1 since the past 1 month ans its been a good learning experience. The classes are 2 in a week with a duration of 2 hours. They also have the option of 1 class a week but a little longer duration. Best is to go there ask them for the batch details.
Im sure there are more places where you can join courses to learn spoken arabic.