If you plan on cruising in the future, I would just go ahead and get a passport for your child especially since it will be required at the end of the year. You wont get it time for your upcoming trip (unless you pay extra for rush service). Im waiting for my newborn's birth certificate and ss card right now so I can get one for her. I also got one for my son soon after he was born.
My son is 18 months and the cruiseline had us sign a form confirming both parents were going on the cruise and if not, what was required, etc. I get the impression that for security reasons, you would be better off getting a passport.
Less hassle and stress always makes a better cruise.