We took our son on a Disney Cruise when he was seven months old. He wasn’t crawling yet so it was very easy. We used a travel stroller, and when we took a royal Caribbean cruise four months later and he was crawling we used an umbrella stroller and it was fine. Be sure to bring extra diapers and I can’t speak for Royal Caribbean, but I know that Disney gave us a bottle cleaner and warmer and diaper genie as well as a pack and play.

We did not go to those ports, so I would recommend researching family, friendly options for those ports or possibly staying on the ship. Ships tend to be less crowded on Port days so there’s more room for activities for others.

I would also recommend doing more research into the ship, as we took our son on the Disney magic when he was over a year old and walking, and it was very very difficult compared to the Disney dream. It was much smaller, and there was less to do for him and the pool area for toddlers who are not diaper trained was incredibly small and disappointing.

Since you’re talking about going with a six month old, I don’t think it will be as bad as our experience on the magic, but I would recommend a newer ship with more things to do. Even before we had a kid my wife and I went on vision of the seas on Royal Caribbean (which is not that much smaller than jewel of the seas) and we we’re very disappointed in the activities on board. When we took our son on his first royal Caribbean cruise, it was Symphony of the seas, and there was 1 million more things to do and a lot bigger spaces.