I want to ask to meet with my partner's therapist before moving in with her
That is an invasion of privacy. Why do you want to meet with your partner's therapist?
I want to learn more about my girlfriend.
You should not feel entitled to speak with your girlfriend's therapist. Instead, you should remember that getting to know your girlfriend comes with the experiences you have with her.
I don't see anything wrong with what I'm doing. I'm just trying to build a healthy relationship with my girlfriend.
I don't think it would be healthy if you knew about things you have no business to. She would feel horrible about it and you would be interrupting her therapy for your own self gains.