Dr. Khudsia has a private clinic on Al Waab street. She is a very good doctor..although there is a long waiting line outside her clinic even before it opens, so make sure you go early otherwise you'll have to wait for a looooong time. she does not take phone appointments, so the only option is to go to the clinic and take a number...
Another excellent indian doctor is Dr. Sujatha in Al-Ahli hospital..She is south indian, maybe keralite or tamilian (i'm not sure).. you can make telephonic appointments at the hospital to see her.. she also gives her patients her mobile number in case of any questions or emergency and attends all her calls..she is really good..!