What documentation do you need to take an infant on a cruise?

Angel asked:

I didn’t need to have her birth certificate when I flew within the continental US, state-to-state, but I didn’t need a passport for myself either. My family is planning a cruise, and we plan to bring our infant daughter. Do I need to obtain a passport for her, or carry any documentation for her identity, or to prove that we are her parents? She will be approximately a year old at the time of the cruise. (Just past her first birthday)