I find it hard to believe that there are only 20K new doctors a year if there are 1 million doctors. This would imply that the turn over time for doctors is at least 50 years and in all likelihood greater given the growth in total doctor numbers over the last 50 years. This is just not plausible.
This is at least a plausible number. While we still have not established if the 10% number has any basis in fact, you would only need 19.3% of new doctors to be muslim to shift the numbers. This still seems high to me, but it is possible.
I am not doubting what you are telling us is what you have found, just that the numbers have to be wrong as it is not plausible that there is only 2% turnover in doctors each year.