We cruised with our son when he was only 2 years old and had a blast. I wouldn't opt for any excursions, just hit the beach, sightsee or do whatever you want with your child. Relax and enjoy your child for what they can do and it will be a very memorable cruise.
Just got off the Explorer on a western Caribbean cruise and they now have a brand new children's program in place for children 6 months - 3 yrs. old. It is the "AquaBabies, AquaTots" program sponsored by Fisher Price. It appeared to be a great success to the little ones onboard this past week.
Nancy