One year is fairly young. As long as you understand that you are going to miss out on some activities and you are willing to leave the dinning room if he acts up (or just eat in the buffet) then I see no reason to not go on the cruise. If he is potty trained then even better as he can be left with his age group in the cruise lines childern's programs.
Also, if you do go on Disney, I'm sure they are set up to handle that age. Many families go on Disney and not all the children in the family are going to be old enough to be solo...
We cruised on a family cruise and our niece was that young. They didn't have a problem. It can be done.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013