I can see why you feel uncomfortable. 16 + 19 fine like everyone says, but the fact is, you're there in a position of authority, and they are in your care.
Do I understand the situation right? So whilst your ages are fine, it's more that it's 'unprofessional' a breach of the responsibilities and boundaries we hold adults that look after children accountable to.
So I would say, remove yourself from the situation if you feel uncomfortable, so that you can date her, without crossing the line. Not the age line, the professionality line.