haha...I know what you mean. Are you from the UK by any chance?

For all non UK people, we call a doctors clinic a doctors surgery - where we see our GP. It doesn't mean we are going under the knife it's where we go for normal treatments.

Anyway, in answer to your question, I think your best bet is the American Hospital, Doha Clinic or Al Ahli Hospital.

This is the website for Doha Clinic:

http://www.doha-hospital.com/Message.htm

I can't find the website for Al Ahli and the one for the American Hospital isn't working but this is the address anyway: http://www.ahqatar.com/ar.php

Good luck.