As this is a carrier requirement, not a TSA mandate, I suspect a school ID will suffice, particularly with a copy the passport (although having a NYS ID card is not the worst idea, generally).

My daughter has flown solo with only her high school ID witthout issue (can't remember if DL or not). If there is no bag to check, the issue of the carrier's ID policy is unlikely to arise at all, as TSA will let her through.

TSA does not require children under 18 to provide identification when traveling within the United States. Contact the airline for questions regarding specific ID requirements for travelers under 18.

TSA Identification