This would be an easy decision to make, except that his twin sister, who is very bright, but not enough to go ahead a grade, would be left behind. I fear this will be a big blow to my daughter's self-esteem, if not now, certainly when she gets a little older.
Perhaps your daughter is also gifted, but has not yet shown her true learning ability. She is still quite young as a kindergartener. You may not know what her future potential will be, based on her current maturity level, personality, and whether she lives in the shadow of a brother with a demonstrative personality.
In my view, you have two options. First, have your daughter tested now to see if she has abilities on par with her twin brother and consider acceleration if warranted. Second, go ahead and grade-skip your son. This recognizes his individuality and doesn't hold him back. Let your daughter know that she and her brother will not always do things at the same time. Emphasize her current strengths to her. Consider having her tested in a year after she has more time to develop on her own -- she may be ready to move up with him by then.