What does the OP’s daughter want to do?
OP mentions her SAT scores, but how are her grades? Does she have any extracurriculars that she would need to stay on-age with, like sports or music?
My son had perfect CoGAT scores twice in math, and in 8th grade due to his trouble with writing (he is on the autism spectrum and has fine motor issues), he barely got through and was placed in regular math. He and my daughter were tested by JHU CTY (SCAT) and he did well enough to take online courses, which he does, but she got 95th percentile for both math and English so won an award from them. She is taking computer programming in 6th grade. My son did well in 9th grade and will be in all honors next year, but the actual school work part is challenging for him; standardized tests are easy for him. He may end up in a trade, or he may end up a history professor.
Personal anecdote: I have a friend who is in a non-tenure track teaching job. She entered college at 14, graduated at 18, and went to medical school. Long story short, she dropped out and got her PhD in a science instead, getting married somewhere in there (the guy is two years older only, she met him when a junior and he was a freshman). She was totally on the fast track and then real life stepped in. She’s not unhappy, but the experience of college as a young teen was stressful for her, and it took her getting to 18, 19 years old to realize that maybe she didn’t want to be a doctor, or make that level of commitment.
My take on this is to see what your daughter wants. There are so many options depending on your financial and time resources, and what she is interested in. You don’t need to “put” her anywhere, but if you have the money, provide extra programs to supplement her learning. I agree with looking at local universities to see if she can help with a professor’s research. There are also supplementary programs with JHU CTY that are very interesting, even ones for the whole family.
PS - automatically approved for JHU CTY with those scores as far as I know. Just apply and send a copy of her scores.