I happened to read this post right after the one about this new T being a Ph.D, which doesn't indicate stupid. You sound like you are very angry and scared and sad about your current T leaving, which is totally understandable - but please understand that this is no indication of the skills of your next T. If you decide to see this other person so soon, know that you will probably process your grieving with this new one. Yes, it is challenging, it is difficult, it can be sad and scary. But I don't think that bringing a friend to your session will help you. You are just delaying the one-on-one session, which I'm guessing is what you're trying to do. But by bringing a friend you will only be bringing one more person into this already messed up situation. This sounds to me a bit like a test for your new T, so if I were you I'd ask myself what you'd hope him or her to say and what you think they should say and how that plays into what you're facing during this time of loss and transition.

That said, it's your right to ask for anything you believe would help. Your T will say yes or no based on his/her opinion on what would be the best course of action for your treatment. Just be aware that there will also be a confidentiality issue - if your friend is there, the T will not be able to talk to you as s/he otherwise might, s/he shouldn't bring anything from past sessions to the table. This could be quite limiting for a therapy session.