Q. The school is not accredited, merely a dance company that teaches ballet. Does this allow/prevent her from being considered a full time student?
A. Maybe.
But, as @Bsch4477 said, the question is academic for the current tax year, since your child was a full time high school student for the required 5 months.
To claim a tuition credit, your student must be enrolled in an "eligible institution" for post secondary education. But, the rules for being a full time student, for purposes of claiming your child as a dependent, are not as stringent.
From IRS pub 17:
Student defined.
To qualify as a student (for dependency), your child must be, during some part of each of any 5 calendar months of the year:
1. A full-time student at a school that has a regular teaching staff, course of study, and a regularly enrolled student body at the school; or
2. A student taking a full-time, on-farm training course given by a school described in
(1), or by a state, county, or local government agency.
