I'll share my own experience with this. I am a September baby, so I would be 4 entering K, only to have my b-day a few weeks into the school year and only just be begining 5.
My parents had me enrolled in a pre-school which had a blended 2/3 year old class, a nursery and a kindergarden. Finances changed, circumstances changed and they enrolled me in the local public school.
Despite testing well, and being placed in the "fast tracked" classroom, the talented and gifted program, and in classroom settings where I, and others who completed their work quickly, could get out of our seats and do supplemental self study, I was often bored and frankly disruptive. I didn't have to study or apply myself to anything until I got to lawschool. Even then it was just a question of managing the volume.
My point being, notwithstanding what you decide re: whether or not to repeat K, be sure to look into the curriculum and expectations of the new school you are considering transitioning her to. It was very frustrating for me to be in a firstgrade classroom where the teacher was still introducing letters, and I would entertain myself by reading the names of the presidents displayed along the chalkboard.
Good luck to you and yours,
F. B.