I would repeat, if needed, in the early grades. It is common for kids to do so, often for maturity reasons, so other kids won't give it a second thought.
Our middle kid repeated 2nd grade. She moved from a private school with an end of calendar year birthday cutoff to a public school with a September 30th cutoff. With an early October birthday, a repeat of 2nd grade placed her in the "correct" grade for her birthday. Plus it was a different school, so no one knew she was repeating a grade (including the teacher, whom the school admin failed to tell - she wondered why she "knew everything").
While we didn't think of middle kid as gifted at this point, we also knew that she could have entered 3rd grade at the public school and handled the academics. Our decision was due to her immaturity.
Is her current school a good fit? Or would it be better to change schools and repeat?
For middle kid, she was bored with the academics for a number of years, but the repeat allowed her to be in with kids more at her maturity level. Looking back, I think we made the right decision (she is now a HS senior). Of course, you don't really know what the "right choice" was for years - just do the best you can, probably best to "go with your gut".
