If she's really going to "get into" trap/skeet then she'll definitely want a 12-ga. For skeet, she'll be handicapped without an auto or an U/O because of the doubles. Since she's small, she might be able to take advantage of a bottom dollar super deal target gun: Beretta's
3901 Target RL youth gun. It's very attractively priced to encourage young shooters. Unfortunately, you're not going to find a decent target gun within your budget.