Yup! A doctor's authorization is sufficient to get a female name, but the government won't recognise your gender until SRS. A bit weird, but it's not so bad, actually. You don't use the gender marker a lot or show it to people, and according to the experiences i have read, things go relatively well, usually. Then after 1 year of RLE, you're good for SRS and you can change the marker.
But this is only Canada. It varies between countries. Some countries change everything you want on one go, some don't even require your doctor's input, and some will require you to pay for a lawsuit to prove that you are female and should be given those changes, and a few don't even permit it unless you have a 100% proved physical anomaly. And it even varies between states in the US, I think.