I don't know where you're located, but here in the states the APA does actually have a required waiting time of 3 months. This is supposed to give your therapist time to make sure you're "mentally okay" as you say, and make sure you fully understand what you're getting into and that it's right for you. That's not to say that all therapists follow the SOC (Standards of Care), and some doctors will give hormones without a letter, but that's not something I'd count on since it's not typical. I would start looking for a doctor now and just see what they want from you.