In rhythmic gymnastics what level do you have to be to go to the Olympics?

probably a professional. Or if the judges think you're good, they might send you to the Olympics, but most probably a pro.

Obviously a professional. And it's not enough to just want to go there. If by the age of (max) 15 you're not already on the National Team then there is no way in hell -unless you are exceptionally talented or rich) that you can compete there.