Yes, there are plenty of activities that minors can take part in on Carnival cruises. Carnival Cruise Lines specializes in family vacations, and that includes things for people under 21, under 12, and even under 12 months. There are three separate children's programs for guests ranging in age from 2 years- 18 years. For those guests activities range from coloring, swimming, and playtime to movie nights and teen dances. For the large part, guests from 18-21 can participate in all activities adults over 21 years of age can, with the exception of consumption of alcoholic beverages, entrance to the night clubs, and gambling in the casino. Off-boat excursions may be age regulated.
For more info, see Carnival Victory Cruise Ship