Similar to Catalana, our school district has an age cutoff for kindergarten, but not first grade. I'm not sure about the rules. We also have a program for early entrance to K so we may be in a more progressive district.
I would call around and see if there are other preschools that are not as strict about age. It sounds like your school is not willing to meet your child's needs. Do they have other reasons for wanting to keep her with 4 year olds? Around here it is well known that the Catholic school takes kids early if they have the ability. Many people have used it as a way around the system.