We used to bring a car seat and would ask the steward to store it for us in him separate storage area. Otherwise the cabin gets too tight. I assume you'll be bringing an umbrella stroller too, right? This will take up room in your cabin too.
Disney is great for little ones. There is a nursery you can leave your child at for an hourly fee. Sign up early on during the cruise for the hours you would like. I wrote an article on it on this site called "Disney's Magical Nursery."
Luisa Frey Gaynor
Family Cruise Editor