I started auditing classes around that age. Having your daughter meet the professor first might help it go more smoothly--he or she will see your daughter's abilities and interest in his or her field--and you'll have a better idea of the requirements for the course. For me, it was helpful to meet with a few different professors to see which ones were receptive to having a young child sit in their class. Another way to get around some of the possible obstacles is to enroll in the class with her--schools seemed more receptive to having parental supervision when I was actually on campus.
You might want to make sure that it's auditing or pass/fail, as any course taken in college will stay on her transcript (required to be submitted for graduate or medical school after she finishes college).
