If your therapist knows that you're trans and you've been seeing her for some time, then you could get your letter very quickly. Some therapists require one visit. Some seem to think that three months is not nearly enough. Most seem to fall between these extremes. My therapist, for instance, let me call the shots and had no trouble writing me a letter as soon as I decided that I needed it. I had my first T shot six months after I started therapy, but my therapist would have written it a bit sooner had I been ready.