Taking a 1 year old on a cruise would be great, but I think I would go the Disney route. Back when Disney was the Big Red Boat, we took our two girls. They were 5 & 3. They hardly remember some of it so take lots of pictures. How could a 1 year old not love seeing Disney characters all over the ship. I'd definitely go Disney route for that age. The Summer would be the best because the port stops would be a lot more pleasant for you with a little one. Remember to take that umbrella stroller........!
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!