B.B.
A shy kid is at 5 is likely to be a shy kid at 6 and 8 and 10. What you are describing sounds to me like this is part of her personality and not something she is going to grow out of. Some people are gregarious, some are not. I was a shy kid at 5 and am now a reasonably shy adult at 32. It's who I am.
I would not have a kid who had completed K (and done well) and was academically ready for 1st grade repeat K. My son started K early, at 4 almost 5, and is heading to 1st grade next year, at 5, almost 6. I wouldn't even consider having him repeat K so that he was one of the older kids in the class rather than the youngest, but I realize that leaves me in the minority. He is also on the shy side, but again, I would never have him repeat a grade for that reason.