(((((((sunrise))))))))))
I am really glad you are so supportive of your daughter getting counselling. I'm no longer really close to being 13, but I can understand if there might be some resistance on the part of your daughter. Perfectly normal actually, teenage thing.

I figure she might not be very open at first, but then again it's hard to immediately "jump in" and trust anyone the first bit in a relationship, therapeutic or otherwise. If your daughter is uncomfortable about going, or has any thoughts about the counsellor, it really is important that you listen to her - she needs to be heard, since this is for her benefit. I don't think a counsellor will refuse to see a person from the "get-go" just because they aren't very open. If it takes a session, then it takes a session. As for your daughter liking her (the counsellor), maybe she will, maybe she won't. If she doesn't, try to get her to make sure of it - and if she still doesn't, then it's just having to find someone else she fits "better" with.
Good luck, and I hope this proves to be beneficial for your daughter.