I am very, very sympathetic to your situation but I'm afraid I do think that it is unreasonable to expect a female doctor to be available immediately.
The surgery where I used to live had only 2 doctors, both male. The area it serviced was approximately 80% asian and it was generally considered to be an odl fashioned asian area eg. the women didn;t mix at all and the girls often went to a separate school but that is another thread.
I actually refused to see the female nurse for smears there as she was very rough, preferring to thave them done by a gentler chaperoned male doctor instead.
I imagine that statisitcally there are less female doctors than male. It is a career after all with long hours, a huge amount of training and some women particurlaly ones with children may decide against that career path or they may wish to specialise.
If you feel that this need is so fundamental to you, which it obviously is and I respect that feeling, then you must register with another practice that has a higher percentage of female doctors.
You are within your rights to request to see a female doctor, you are not within your rights to demand that it is within an unreasonable time scale.