So much depends upon your child and the schooling available to them. Typically, parents know their child best and if able to look at the situation objectively can assess the readiness of the child, especially if the child has already been in preschool ( if the preschool has teacher conferences).
As others have mentioned, you have mental, social and physical maturity and it is the lucky parent who has a child who has balance between all three at just the right time.
Anecdote- one of my children is a summer birthday and was academically very strong. She attended a parochial preschool and kindergarten because the teacher/student ratio was quite small and it helped her hone her social skills. Upon entering public school for first grade, we encountered a problem: she was reading at high school level and her math was intermediate school level and they had no gifted accommodation for students like that (small city of about 23,000). They wanted to put her, a 6 year old, in 3rd grade. Many third graders are 9, with the red-shirted students turning 10. We said 'No way!' and they ended up doing a pullout for her where she spent a few hours with the older students and everything else on grade level. We moved after that year, and things were much improved. We wanted her to continue to enjoy learning and there is such a fine line between challenge and futile stuggle because the young brain has simply not got the maturity to understand the context.
That doesn't delve into the physical side of redshirting, which can be an issue for both genders, but probably moreso for boys. All of my children started at their age appropriate grade level, and with our family being late bloomers physically, I can see how it affected them in athletics but frankly, I am never going to put sports over academics. Sports are great and a marvelous opportunity to learn, but in our family a sport isn't going to put food on the table.
Best of luck with your decision. The fact that you are thinking about what will be best for your children and their education already puts them on the right path.