We went to Alaska with a 4 month old and a 2 1/2 year old. i would not do it again. We didn't get much enjoyment out of the cruise. Also, did you know you have to pay FULL PRICE for the kids for the cruise and for most excursions. Yes, full price for a 4 month old who was nursing. Also, the strollers are IMPOSSIBLE to navigate through the passageways on the way to your room and back. Another problem is dinner time. If you eat in the formal dining room at night (which I think is one of the best parts of a cruise), you might not get the first seating and be stuck eating at 8:00 pm. In addition, being served all the courses takes up to 2 hours (a long time for a little one to sit). Another problem is the railing overlooking the pool decks are not really designed with small ones in mind (my daughter could have easily fallen through). In addition, there are often crowds, making losing your little one a possibility. No bathtubs mean showers only for the little ones. The rooms are quite small, so think about where the baby will sleep.
We have been on many cruises, so I know how much fun they CAN be. If this were my only chance to take a cruise, I would DEFINITELY go, but if it can wait, I would DEFINITELY wait, especially considering that you are paying FULL price for the two kids.
If you decide to go, a suggestion - we made a heart shaped dog tag with our daughter's first and last name and our cell phone numbers on it and tied it into the laces on her shoe. We told her to show it to someone if she got lost, because that is a possibility on such a trip. Also, you can give Benadryl to children to prevent motion sickness. It really works. Just ask your doctor for dosage.