yenting: the best answer, is ask your father! maybe the minhag came about simply because you enjoyed doing it and isn’t really a mesorah at all!
For all practical purposes, women/girls are generally yotzei with their father/husband. I think I remember lighting once – in Pre1A when we made a menorah in school. My daughters light their arts & craft ones. Once they stop those (1st grade I think) they stop lighting. My boys light.
As to the lighting at the z’man, even below bar mitzvah boys should light then even if the baal habayis is not home yet (yes, we asked our LOR).