You are intertwining multiple issues. Simplistically, since you are homeschooling, you determine grade level. If you want to call 7th grade 9th, if she is doing high school level work, you can. She can graduate at 15 having completed high school.
Depending on your state, she might not need to take the GED. Depending on your POV, she will have the stigma of the GED. (I personally would much rather my kids have a high school diploma than the GED.)
All that said, I have some very advanced kids and we don’t graduate them early. It doesn’t mean they spend high school completing high school level courses. They take appropriate level courses. For example, I have had a student graduate with credit for multivariable, diffEQ, linear alg 1&2, cal-based physics 1&2, modern, physical mechanics 1& 2, etc. He dual enrolled at our local universities.
What schools do you think she would apply to? Graduating early with a GED will put her at a serious disadvantage for admissions at competitive schools. There are ZERO bonus pts for graduating early. None. She will be competing against equally advanced kids who have accomplished far more academically bc they pursued 2 more yrs of coursework and have additional yrs of outside pursuits on their resumes.