It's a balance of harm issue, really.
It would always be better socially, in the English system, for a child to be educated in their own year group with good differentiation However, the difficulty of delivering the right education for that child gets greater as the distance from the 'norm' gets greater, and at 3, 4 , 5 years either side of that norm - ie genuine outliers - it becomes more possible that delivering an appropriate education won't happen all the time, or will happen to a more limited extent.
So for those outliers - like the pre-verbal 9 year old I taught who had been held back a year, or the 9 year old doing GCSE level maths, the balance of 'educational harm' vs 'social good' switches.
Exactly where it switches does depend a little on the school and the child. Both the outliers iI mention were socially unusual anyway, and their lack of integration was likely to be as acute in their 'altered' year as in their 'normal' year. I Had another child in the same class as ther 9 year old who was almost equally delayed in terms of their learning, but was mucgh more socially integrated into their year group, and in that case the change of year would not have been appropriate.
In the OP's case, because of the size of the school and the apparent low ability of both the Y1 and Y2 cohorts (as OP says that her DD was higher even than the Y2s), if she were to stay in that school forever, it might be appropriate to accelerate her because she is 3-4 years ahead of her 'age peers'. The problem arises because she is not very far ahead of any more representative group of age peers, in fact in line with up to half in other schools, and so problems of transition become acute. To be put up a year and then to be behind her peers in the new year once in a larger and more representative group would seem to me to be a very difficult situation.
I was accelerated a year, as I said earlier. However, I remained top of my new year group, even in a highly selective school and then university environment.... but even so, I would have benefitted from NOT being accelerated.