My daughter is younger (7 in second grade) but we did whole grade acceleration after the first quarter of kindergarten. After she was moved, I had my doubts as to the wisdom of the decision, but she has adjusted well and is now at the top of her grade in terms of achievement. As it turned out, she was diagnosed with ADHD after she was moved to first grade, but she has done well despite that (probably because she responds well to meds). So even if there are some challenges, a child can adjust and do well. A lot of it is peer pressure and not wanting to stick out as being immature. Kids feed off each other and want to do advanced things like the kids they are with. If they are the top kid in the class and no one is at their level, none of that is going on. She started acting a lot more mature immediately after she was moved.
Of course she is younger, and it is probably easier the lower the grade. My son who is in kindergarten is very advanced with reading and math but I wouldn't move him up a grade because he is way too immature with certain things (like motor skills) and his motivation level is lacking. It depends on the circumstances and the child's strengths and weaknesses. If your son is in favor of it, then that is a very strong reason to try it. It's a hard decision to make not having a crystal ball.