I had a little different approach...for perspective, DD is averaging 2 grades ahead in achievement and it looks like she will be somewhere in the neighborhood of 99.8% for IQ. I told her to just go to kinder and have fun and make lots of friends. I supplemented at home with whatever interests she had. I did not give the kinder teacher much of a heads up and they figured out pretty quickly that she was ahead. They started having her spend 20 min per day with the reading teacher and brought her to the attention of the gifted teacher (who usually does not get involved until 3rd). The school is doing many things right and could be doing more...but she will most likely be nominated for the districts special classroom with the top 1% of students. Because of the available programs in place, I have not advocated for grade acceleration...she only has one more year before the special program starts and all the teachers and administrators at the school know her and are watching out for her.
For us, it was the right decision because dd had some sensitivities that she worked through with age and she learned some good socialization skill and I figured that it would be a good year for the school to get to know her.