Yes. You should obviously break up the natural friendship groups because of one child, who only has no one because she prefers to play within her tiny year group, and the other "lone girl" has now made another friend.
The world does not revolve around DD. OP is teaching her it does by insinuating that two girls forming natural pairs, and her DD not being one of those, is bullying. You can see her dislike of this "new girl" and how she "found out" that they were doing after school activities together from her OP. Literally it reads like she thinks this little girl is cheating on her daughter.
The two girls played together before, because they were the only two left over. It doesn't look like the other girl was naturally drawn to DD, given that another girl has only just started and they are immediately doing out of school stuff with her (presumably she never chose to with DD or OP would have let us know this).
I'm sorry if its hard reading OP, but it's a fact of life that people will prefer others over your DD. It doesn't make them bad, or wrong, there will be people who prefer your DD, she's just in such a tiny year group that because Alice likes Jane, and Susan likes Claire, that's everyone paired off.
And no, I won't teach my children that they must continually play with people they don't want too, because the other child wanting too has a greater right. They don't.
As long as my children are kind, they can choose their friends. "Why do we have to play with Peter? He always wants to play robots, it's loud and we don't like it, and no one else wants too"
"Oh but you must, or Peter won't have anyone to play with"
Actually. Peter needs to understand that, if no one else wants to be that loud, he can either a) be loud on his own, no one's stopping him, or b) he doesn't get to dictate how anyone else plays, so he can join the other children, playing tag (or whatever) because that's their choice.
Peter's rights do not trump anyone elses.
Imagine DD being told "you must play football at lunch"..... "But, I don't like football? I don't want to play football. I am not friends with the people that play football."....."yes but Peter wants too, so you must"
You wouldn't expect that of DD. Why do you expect it from other children?