My neighbor did this. She moved here from California during the school year. Her daughter had started K in CA. They gave her a really hard time. This is for a VERY articulate child who was writing well even in K. She got sick of the back and forth and chose to keep her in a private K, and she seamlessly moved on to 1st in FCPS. Her daughter has a November Birthday. My daughter was thrilled as she has a late September birthday and was always the youngest before this.
Side note: The girls are both in 3rd now in an AAP center so academically it has been just fine. Our neighborhood school does not have much red-shirting though, that helps.