The Islamic Cultural Center (aka Al Fanar) near the souqs has a great dawa center and caters to English speakers. Not sure if they have classes in Urdu. Dr. Bilal Philips is the Imam. Visit his website for more info: http://www.bilalphilips.com or call +974 - 5383991.

He also runs the Qatar Guest Center: http://www.qatarguestcenter.net/

InshaAllah this info is helpful to you.