Just remember that cruise ship pools are not particularly large and are more about a quick dip to cool off than they are about swimming - especially on the at-sea days when it can be standing room only in the water.
We took our son on his first cruise - aboard the Celebrity Century - when he was 20 months old. I'll agree we were limited. At that time, they took kids at 24 months in the youth program, not that it mattered. It definitely is a better experience when the kids are older.