Wow. Okay, here goes. I am the parent of 2 gifted students, now adults, and have an extra certification from UCLA for teaching gifted students.
Do I need to just wait this out and hope she progresses to Kindergarden or do I leave her in Pre-K for another year? I do not want a bored child academically but I don't want an emotional wreck due to the social age difference.
First: asynchronous development is typical for gifted kids. Intellectual, physical, and social-emotional development do not happen at the same pace. It is characteristic for gifted kids to be advanced intellectually and actually delayed socially.
Also, gifted kids do not always relate well to peers their own age; they tend to relate to older people.
I would not be too concerned about academically bored 4-year-olds. I'm not saying that she shouldn't be learning anything she wants to learn or is ready for; I'm saying that her time in a Pre-K should be spent developing social skills. Learning to listen, to cooperate, and to work in group settings. All of those things that are difficult for many gifted people of any age.
I also wonder what kind of "work" she is not progressing with. Is it that she can't do it yet, or that she already can and just doesn't want to?
I'm not sure what sort of school she is in. Or what the philosophies are, or the training, or the program, or the expectations. I hope, at the age of 4, it is about discovery, exploration, and learning some self-management, organization, and cooperation with others.
Have you looked into your local Montessori schools? I've had gifted students who thrived in that setting for their preschool and kindergarten years.