My son has been on 3 New Years cruises (11 mos, 23 mos, 35 mos), and will go again this NY (along with a new baby). At that age, I think its easier to deal with a child on a ship as they can actually sit still (or fall asleep)! I dont know how much he remembered after the first cruise, but he remembered after the second one. Every time he sees an ad on tv he announces that we have to go back to the ship and take a trip to the beach. We did take lots of photos, and bought a ton from the ship (portraits and cameos) and my son loves looking at his photo albums. It really seems to help him remember. Just be sure to bring along all his supplies (lots of diapers, sunscreen, hats, swim diapers for the beach (not allowed in the pools), infant medicines (Tylenol, Motrin) child size bandaids/first aid stuff, snacks, sippy cups, small utensils, dishsoap, beach toys, favorite animal/blankie.......its a lot stuff but well worth it!
alison