Hi Brent,
Welcome to the Moms Panel! I know exactly how you feel - and I'll even admit that I considered canceling our first cruise with our toddlers over my irrational fears. I am so thankful that I didn't. I have found our Disney Cruise vacations to be the most enjoyable, relaxing (as possible with little ones) and FUN vacations that we can take a s a family.
I love having all of the fun and excitement that we can tolerate, knowing that the quiet comfort of our stateroom is only steps away should a meltdown ensue or a nap be required. There is peace of mind knowing that you can find fresh, prepared, healthy foods for the little ones at any time of day - without having to make reservations or figure out transportation.
Of course my biggest fear was always my little climbers - I would lose sleep worrying about these adventurous little tykes. I was impressed by the kid-friendly function of the ship. The verandas are covered by plexi-glass, which inhibits the ability to climb the rungs. The railings were higher than I anticipated - and you can request that your verandah furniture be removed if you are concerned about children climbing on them for a better view.
I compiled a list of things to pack with your little one, you can see it
HERE. It's also worth mentioning that DCL has partnered with
Babies Travel Lite to offer guests traveling with little ones the opportunity to pre-order the baby products they need, and they will be delivered directly to your stateroom.
I hope this helps!