Hi from North Carolina. I was a gifted program kid (now and adult) in this glorious state and have had plenty of encounters with children since who are in the program. I even went to the North Carolina School of Science and Mathematics. Go for it with the more rigorous academics BUT the thing you'll need to enrich in the home environment is those social and emotional lessons. They are getting deprioritized in favor of academics and in order to succeed in the world, the ability to people is actually more valuable than the ability to scholar. But if she isn't challenged in the classroom, instead of learning how to people, she'll learn how to be in trouble due to very appropriately suppressing her frustration and boredom as much as her age can possibly do ... which isn't enough.

Also, if she's any kind of mentally healthy, don't send her to NCSSM, no matter how much she begs. That's where people go to have massive mental health issues. The only people who did better at that school, and I am one of them, were people whose home lives were so challenging and unstable that the school was actually an upgrade. Any alumnus - except the ones specifically chosen by the recruiting office, of course - will tell you the same.