I do a lot of dream work as part of my therapy. (my t has a thick folder full of my dreams that I've typed up for her or emailed her over the years.) If you don't know her thoughts on dreams and dream work, you could ask her. Or even just share a really bland dream with no embarrassing parts first, just to test the waters.

(My dream worker self does not think it is random or irrelevant, but then I'm very very into dreams and dream work!)

I don't know if I would have shared something like that really early on, but if I had a dream like that now? I would absolutely tell her but then again we've been working together for going on 6 years. Still, I have had some doozies where I turn about 15 shades of red reading them to her haha. When we work on them, she has me read them out loud and then we discuss them.

Maybe you can ask her what she thinks about dreams, and if she seems open to discussing it, you could kinda introduce it a little by saying "there's a really embarrassing sorta sexual element to it and I don't want to freak you out or anything" and see what she says. Again, I've been with my t a long time, so you might not feel comfortable enough yet to ask that. I dunno. I'm half asleep right now so really rambling. Sorry. I also tend to get carried away with the subject of dream work. I wish you the best whatever you decide to do!