It's a dream, no more under your control than the rest of your unconscious. It is supposed to be helpful to you, show you things you might want to discuss with T (and give you a way to discuss them). T, I think, would be thrilled if you'd tell her the dream. I told my T my dreams about her, including the one where I had my head in her lap and she was stroking it! and one where she was a co-lesbian with a group therapist I'd had 10+ years before (neither were lesbians :-) etc.

Your T will probably have some ideas what the dream might mean that you haven't considered? I always was afraid of being late for therapy and dreamed about it a few times; had to stop once and do the "right thing" and be late or continuing on to therapy and not help the people who only I could help (I stopped :-)

Googling T is not stalking. Stalking would be literally going to her house and following her, in person. I use to look my T up in the phone book, regularly (and myself :-) to make sure she still existed and reassure myself. The first time I saw T in a new place, she wrote a note to me, personally, and put it on the outside door to tell me how to get to her exact office and I kept the note in my wallet for a year or more (and then gave it to her, discussing having kept it). There is lots of good things to discuss with a dream between you, helping with the subject matter. You can talk about not liking to be late and worrying about it (I could not understand for many years, why being a couple minutes late would bother me so) and why you feel bad wanting to know more about T, be close to her and are looking up her address, etc. It can be very helpful to your therapy.