Just so you know, in New York (as well as many other states) teachers are mandated reporters, meaning they have a legal obligation to report child abuse.
HOWEVER (bold, italic, underlined): If Halacha conflicts with that, there is no question that someone in such a situation needs to follow the Halacha (Da’as Torah) over the law. I just wanted to make you aware of the fact.
Personally, my own Da’as BaalBatim (worth diddly squat) is that if the father is not involved with your student or any other kids, there is probably no Halachic basis for saying something.
Hatzlacha, and even if your student doesn’t realize all that you have done/are doing for her, there is certainly Someone upstairs who does!