If you said that your daughter would be remaining in her same school, my answer would be different but as you have the opportunity of a new school, I'd see nothing wrong with retaining your daughter in her current grade - so long as she is helped to feel comfortable with it.
Children develop at different paces - some children have underlying issues that slow their development. To know if that's the case, testing could be done. You don't say that your daughter is having academic issues as well. In either case, it never hurts to consider all options - what would be her options at her new school for special services that would help her with her issues?
Another approach - if possible- is to go and observe at her new school. You might find their third grade inappropriate for her or you might find it to be the perfect place. There is no way to compare one school's curriculum and instruction to another's even within the same state. Schools and their instruction vary tremendously from community to community and one's school's 4th grade is the next school's 3rd grade. To figure out what's what and which is better for your daughter, go and observe in the new school if you can.
In general, experts don't recommend retention. When you say maturity is an issue, is your daughter young compared to her classmates? (ie, a late summer birthday?) Does she have any diagnosed attention deficit or learning disability? While it would certainly be better not to repeat a grade at the same school as before, if your child is otherwise academically successful, she might find the material more boring, and if her "maturity" (behavior?) is already a problem, she may find it even harder to act responsibly and pay attention.
Can you share a more about what kinds of things she does, that make you feel it's a maturity issue?
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