hi! the best place in Doha is Fanar (spiral mosque) near souk waqif.. it is free and the teachers are excellent! the classes are 3 times per week and you can choose morning or evening classes. you just have to go and register which is easy then you will join the next session. you can also learn about Islam in a seperate class if you like..

sunday 5 to 7pm
tuesday 5 to 7pm
thursday 5 to 7pm

or you can do 7 to 9pm (same days) or mornings..

GOOD LUCK! :-)