I agree on waiting until they are 2. I see so many parents with very young children on cruises and wonder how they manage it. If you can't send them to camp carnival for some "down time" for yourselves then it won't be much of a vacation.
Timc makes a good point but I know its not always practical to leave young ones with family for a long period of time. We did it with our nearly 2 year old and my wife was a wreck the whole cruise worrying about her. So even if possible it is still not a good solution. I say wait until they are 2 and then go and enjoy yourselves the best you can.
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