It is not permissible for a woman to lead a man in prayer and his prayer offered behind her is not valid, because of a great deal of evidence to that effect, and the man must repeat his prayer.

It is not Sunnah to recite Qunut in Fajr prayer all the time. Your prayer behind an Imam who recites Qunut in Fajr is valid, but if there is someone who does not always recite Qunut in Fajr, it is better to pray behind him, so as to follow the Sunnah.