I like the way you and your DD handled things. It is tough, esp when the other child maybe isn't as socially "saavy" for lack of a better word, than your DD and her friends. It's nice to see that she's going to try and befriend the other girl,. and that they aren't being mean to her, since girls that age (and I speak from experience) can be quite hateful.
I can relate, but only because I was the other girl when i was younger. We moved right before 4th grade, so I was 9, and I was a painfully shy, socially awkward kid with no self-esteem. Try as I might to make friends, it seems like every time I thought I was connecting with someone, we'd do something a couple of times, it would fizzle. I desperately wanted to have friends, but I can honestly say for 3 years, until jr. high, I had very few. I didn't have birthday parties since I knew no one would come, and wasn't invited to one during that time either. It was a tough time, and I wasn't very happy then. And we also remember.
I also have to say, even now, as a 47-year old woman, I still feel like if I ask people I don't know well, but would like to get to know, if they want to do something socially, they're going to look at me and say "why would I want to hang out with YOU?"