I don’t have enough info to respond specifically to your daughter’s situation.
I can tell you , having been through it myself, that a small insular high socioeconomic status school is not a good setting for a child who is not a social butterfly, especially when they enter midstream.
I was so miserable and isolated when I entered that setting, in 7th grade. By 8th, after trying so hard and not making real friends there, I realized that it was a mismatch for me. There were only 40 kids in the grade, 20 had been together since first grade, and virtually all of those 20 came from wealthy, insular, related families. I tried to explain to my parents that I thought that I would be better off at one of the excellent city exam schools, but they were a long commute on public transit, at a time when the city was very unsafe, so my parents would not let me apply. Four more horribly unhappy years, as the school outcast. I wound up seeking friends and additional education in an after school/weekend special interest program.
Funny thing happened. The summer before senior year, I went to an Ivy’s summer residential program. So did a few other kids from that high school. I immediately made lots of friends there, had a wonderful summer. They didn’t. They were scared of the new environment, couldn’t adjust. I had nothing to do with them all summer, was too busy and happy with all the new friends I had made. But the one kid in the class who would talk to me (as long as no one else was watching) told me that the other kids from the school who were at that same precollege program had written home (in those days people actually wrote letters) saying how strange it was, that I had adjusted so well there, was popular there, while they were having such a tough time of it. He told me, “They’re jealous of you. You’re the smartest kid in the school, you run circles around them in classes, and you’ve got a life outside of school. They’re all terrified of the outside world.” I didn’t believe him, but looking back, I think that he was right.
Sadly, he didn’t adjust to college. He lasted all of two weeks at RPI, then ran home. I don’t know how many others had the same trouble, but when I spoke with a teacher from the school a year later, he told me that a number of my classmates had had a lot of trouble adjusting to college.
If your daughter is miserable there because it’s such a small school that she cannot find people with whom she has something in common, she might be happier, socially, at a larger public school where she is more likely to find a peer group.