I cruised with my son when he was 1 year old. We are a month away from cruising again, this time my son is 2.5 and my daughter is 1. For us with the kids the ages they are, a
Disney Cruise is our number 1 option. That nursery is so awesome!! My son LOVED the nursery on our last trip & he had never spent a second in a daycare before! They are so awesome. It's like a full fledged daycare. They'll feed them, change them, play with them, they have a room for naps full of cribs. Characters visit them in the nursery. It's so awesome! We had such a great experience with our son last time we knew a Disney cruise would be the perfect trip for us this year since they're both still so young. This trip coming up, we chose the late seating and booked the kids in the nursery during it so my husband & I can enjoy dinners together each evening stress free. We're planning to keep them in the nursery pretty late so we can enjoy the evening activities for the adults. We'll just send them with pajamas and ask that they be changed into their pajamas. If they want to sleep they can, but if they want to stay up that's fine too. We also booked two snorkeling excursions and have the kids booked in the nursery during it. We could never do that elsewhere.
Also, they offer lots of other activities for that age...playtime with some of the cruise staff, a morning dance party with the Disney Jr characters, character breakfast, open house hours at the nursery where you can go in the nursery and play with your children in there.
They are not allowed in the pool, slides or AquaLab while still in diapers. However, they have a splash area meant for kids in diapers. My only advise would be, if you have kids in diapers & plan to swim a lot, stick with the Fantasy or Dream. The Magic & Wonder's splash area is tiny and there's not much to it. The Fantasy & Dream's splash area is awesome! Big, lots of different interactive areas, a slide... way better. We'll be on the Magic next month but a very port intensive cruise so it shouldn't be too bad. We also plan to do some resort day passes at some of the ports so we have the option of pools & the beach, along with creature comforts like clean bathrooms & changing tables.
We bring a good quality umbrella stroller...it fits under the bed and doesn't take up too much room in the elevators. I would never bring one bigger than that, but I definitely wouldn't go without one. Even if just for the ports, but also my son would nap in it up by the pool.
DCL lends strollers as well, but they have a limited supply. They also supply diaper genies, playpens, bottle warmers & sterilizers, and bedrails for the rooms. The waitstaff blends foods for young babies so no need for baby food. The nursery provides snacks, milk & meals (there are set times for lunch & dinner). Really, they've thought of everything.
*Tip I learned through our swimming school. Get the reusable swim diapers & layer either a normal disposable diaper or disposable swim diaper underneath the reusable. It provides extra absorption and when they go number two, you just throw the disposable out & put a new one underneath the reusable.