I don't think it's an unreasonable request, I think journaling is a very good exercise. However your thoughts are still yours not hers, so I don't think you should feel obligated to share every detail. I journaled regularly during my first year in therapy. It helped a lot. I would bring it with me to help guide our sessions, but rarely did we actually read together. I left my journal at her office once by accident and she locked it in her drawer and left it in there until I could get it, so it was clear she respected my privacy as well.