I couldn't find much, just that it's $8 per the application: https://www.dmv.nh.gov/sites/g/files/ehbemt416/files/inline-documents/dsmv450.pdf. She might have to just call the DMV.

Out of curiosity I looked up CO and they too require some form of license for a moped (or low powered scooter as they call it): "Owner/Operator must possess a valid driver license or minor driver license (42-2-103(2)(a) C.R.S.)."