Oh so sorry ixis our children's pain is our pain isn't it. I haven't experienced this problem but my DIL is a teacher in Yr 6 primary. She says that there is always trouble with the girls in the friendship groups and they fall in and out with each other on a regular basis.
I think in Yr 7 they are all trying to find their feet in "big school" and I noticed that you said some of her old friends are "still nice to her" but a couple of the other girls (including previous best friend) are rejecting her. I think that these 2 girls might be "queen bees" and the others are feeling insecure and don't want to lose favour with the queen bees, hence they are only rejecting your DD because of the attitude of these 2 girls.
My DGD is now in Yr 10 and we talk a lot about friendship groups (she's at an all girls school) and she tells me about "Miss Popular" and her little acolytes. She says it is pathetic, if Miss P laughs and finds something funny, the others do the same, and even check sometimes to see Miss P's reaction to something before they react. My DGD is very observant!
Why these 2 girls are behaving like this may well be for the reasons you've stated - that DD is young for her age, being summer born and the others are trying to be "grown up" now they are at "big school"- I think Older has given really good advice. Is there a head of Pastoral Care who you could talk to in confidence without your DD knowing, as she is sure to be embarrassed about this being brought up at school.
I think it always looks like everyone else is ok and has a good group of friends but this isn't really the case - I think DD's self esteem is low as a result of this period of adjustment as you acknowledge and then it is easy to think everyone else is ok and you're not.
Given that there were no difficulties in primary school, I feel sure that things will level out over time, it's very early days. In the meantime I don't think you can go far wrong by following Older's excellent advice. Does she have a smart phone incidentally - if not she needs one because they message each other on these all the time!