I wouldn't redshirt under the OP's conditions. Plenty of children are immature, in terms of following directions and rules in class, in kindergarten and even in first grade in my location. I wouldn't want to take a gifted child and widen the default academic gap even further.
I was reading recently (on a fundamentalist Christian homeschoolers' forum) that in some areas redshirting is the norm. That makes zero sense to me academically-- parents who follow the "Outliers" mindset seem to have succeeded in those areas in simply delaying the start of academics for everyone by a year. That's no way to get ahead academically long-term, especially for gifted children. On that same website it was mentioned that this is sometimes done for athletic reasons; I'd never do that with a gifted child, with such a pre-existing mismatch between age and academic level to start with.
Acceleration, and especially radical acceleration, by its nature often involves increasing the apparent effects of asynchrony due to placement with older children. Research shows that it can still work quite well for highly gifted children. That means to me that DeeDee's approach is the best one generally-- support as necessary while you do your best to meet academic needs.
