I guess I'm not sure what you'd say exactly to the teacher? There's no bullying going on. And this other little girl has made it clear that at least for right now, she's not interested in being friends with your daughter. So what's the problem? This is all part of life.
I know it's hard to see your child upset and have other kids not return her friendship and kind words. However you said at the beginning of your post that you are trying to encourage your daughter to be more in charge of her own destiny at school. So why get involved with this?
From what you've said the "worst" thing that's happened so far is that you say your daughter was blamed by this little girl, and then the teacher for hitting. No note. No detention. Nothing.
If you're thinking of getting involved due to the "potential" of this situation to get worse, I'd wait. It doesn't seem like this other little girl is seeking out your daughter to bother her, physically threatening her or anything that's out of the ordinary of normal kid stuff. The reality is that not everyone is going to be friends with or even be nice to your daughter. No matter what you or the teachers do.
I think the best thing you can do for your daughter is NOT make a big deal out of any of this and this other little girl "rejecting" her. Keep her focused on her friends, being nice and having fun at school. If you are optimistic and don't drain all of your energy on these few negative things, then she will learn to do the same thing.
Now as a parent, do listen if she comes to you again complaining about this other little girl or the teacher reprimanding her. Do validate her feelings and talk about how she can handle herself in those situations. But I would only get involved if you think that she is being "threatened" in some way or if the teacher is not being fair. And even then, I would ask instead of accusing.
Best wishes. I know it's hard to watch kids struggle.