We took our 2 year old on the May Transatlantic last year.
He LOVED it. There are so few children in total on the cruise (I think there were 200 all up) that they get so much special attention.
The nursery had days where there were only 1-2 kids in (if I remember correctly there were < 15 nursery aged children onboard), so the staff were able to really get to know him. We got photos, drawings, etc. They were really able to tailor things to him.
Wake Up With Disney Junior often had just him there, so again, lots of attention and fun.
Open House in the Club was also very uncrowded. He was often the only one playing in Andy's room.
Character interaction was amazing! Once they got to know him (and his 6yo sister), all the characters were calling him by name. As a lot of the characters' friends act as CMs in line, even if the actual character didn't know them, the CM was able to say things like 'Cinderella, this is James'. Nothing like a Frozen obsessed boy having Anna and Elsa say "James! How lovely to see you!" when you walk in.
It was a bit cold to swim a lot of the time, and he wasn't toilet trained, but he did spend a few times at the Splash zone.
He is still asking when we're going back to the Mickey Ship as he had so much fun.
Hope that helps.