This is a picture book, not a chapter book, read in 1964/1965 from a grade 3 classroom.
My memory of it may be faulty as I was 8 when I read it.
Girl is unhappy in her village and a misfit; one of the pictures shows her running with dark hair streaming behind her. I remember the illustrations as being dark but beautiful, and the implication was that that the girl was a changeling.
Not “The White Ring” or “The Moorchild”.