Congratulations! We have been homeschooling since kindergarten - also for non-gymnastics reasons. As a former classroom teacher, I can honestly tell you that homeschooling does not necessarily mean closing doors - it means others are opening. Homeschooling isn't an inferior style of education to brick-and-mortar school - it is just different. If my kids went to public school, they would have "missed out" on several opportunities they have gained by being homeschooled. On the other hand, yes, there are things they have "missed out" on by not being in public/private school, but we just see it as a matter of choices and this is what we have chosen.
Before my kids went into 9th grade, I was freaking out about the NCAA thing. The requirements actually aren't too bad, but it can be tedious with all of the core course sheet write-ups and specifics with regard to what they will and will not accept. We ended up using Bridegway Academy because they give you an advisor who is NCAA-specific and helps you wade through the process (and does a lot of it for you). The advisor knows ahead of time what kinds of curricula NCAA prefers if you want to choose your own curricula, or you can use whatever Bridgeway recommends - there are a lot of choices.
Something like Bridgeway isn't necessary, though - it does mean you will have to complete all the core course worksheets on your own and you have to be sure the curriculum you choose is NCAA-approved, but you can totally do it. Spend some time on google - there is a wealth of info out there and MILgymFAN gave you the right link. You are welcome to PM me if you like.