Deemee, I have an august baby, the youngest etc.
At your daughter's age, mine spent half the time in nursery, half in reception, because they would have been her colleagues, trying to make transition easier etc.
I always had a few basic rules when it came to my daughter, one of them being I always believe her. So if there were problems which came out before bed, all muddled up or very very clear, I always took them up with the school or other parents. Still do.
What I have learnt is that academically august babies are just fine, emotionally they turn into a right mess at times.
I gave her the benefit of being the youngest etc till the age of 8. Their social skills is not as advanced as her peers, even if we are only talking 6 months difference. I considered all equations of the problem, I cannot fight for her, but I can teach her, take her part, discuss and lead by example. I made great friends with the parents I considered to be on the same wavelenght as me and we tried to guide our children. At about the age of 5-6 it all exploded back in our faces, all the late evening telephone conversations, oh dear, they fell out, they hurt eachother, what shall we do, orchestrated outings together etc, embarassment etc....the darn kids were at eachother's throats and we were in an impossible situation, we were friends...so we moved the coffees from after school to mornings: nevermind them, we're still friends! Only to be gobsmacked few months/weeks later by the amazing friendship they rekindled of their own accord, actingf like nothig has EVER happened, with an:'you, grown ups are downright weird' expressions on their angelic little faces.
So we learnt...to ignore them.
Yes, we talk about how did it make you feel, what do you think could be done etc...but we're staying out of it.
Unless there are massive problems, like bullying, wetting the bed due to stress, physical violence....I would not move her, she'll carve her own path, under your watchfull eye.