Let me preface this with the fact, I haven't been on a cruise with our little ones. But we did lots of research trying to find family friendly cruiselines: Carnival, Cunard, Disney and Royal Caribbean seem to be the most friendly. However, if your child is not potty trained apparently Disney is the only cruise line that will allow this child into the pools on deck. (The water filtration system is the same for all pools and swim diapers are not acceptable for containing wastes.) We also tried to find a cruise that provides child care for an excursion or even dinner service, and this only came with Specific Cunard, and all Disney Cruises. Nevertheless, we opted not to cruise with our 14 month old twins. I don't know if this information is helpful to you, but good luck either way, and please let me know if you have found anything different on your travels/research.
W.