We've gone cruising with twin toddlers and what we found work well for us:
1) Packing. We got a large diaper box, opened it and removed some diapers and packed it back with food, snacks, and wipes. Then just slapped a baggage label on it. Very easy and then you don't have to drag an extra piece of luggage around. Also will survive an airplane flight if that is how you get to the port.
2) Umbrella stroller - small, light weight, easy to get on and off the ship. Don't even think of bringing a full stroller. Small is important so you can go on "walks" around the ship and not have an issue navigating the more crowded sections.
3) Call for the crib. Your steward will set it up for you every night with fresh linens. We actually elected to keep ours out as it was easy to store stuff in or allow for an quick nap.
4) While many did flex dining, we found the fixed time dining worked well for us as the waiters had the high chair setup ready to go and some kid friendly food as soon as we got there. They also got in the habit of getting our order in quickly. This allowed the kids to eat quickly and not get bored waiting for slow service. So many of the wait staff have young ones they've left behind at home your toddler will be treated like loyalty.
5) Take advantage of the family play time at Camp Ocean/Carnival whatever they are calling it these days. While you can't leave the child unsupervised, they have tons of age appropriate toys and play spaces for a toddler. Take turns so Mom and Dad can each get some individual private time while the toddler is happy distracted with the other parent!
6) If you can afford it - book a balcony. It's a great escape if the toddler gets overwhelmed with noises, crowds, etc. Some of our best memories are just hanging out on the balcony and letting the kids crawl around in peace. It was also a great place to keep on the staterooms trashcans to drop diapers in.
7) Excursions. You really got to know your kids and what they will tolerate. When searching for excursions you can indicate if you have a toddler - quite a few will let a toddler go free or at a reduced rate! We had success with short bus tours and beach excursions. We also did a few private beach clubs where we took a taxi - just make sure to stay in your comfort level. Even did a sting ray swim and the twins loved it - be we made sure the boat had appropriate sized life vests before booking. But again it comes down to what they can handle. Nothing will be more miserable for you and your companions if stuck on a day long excursion and the kids is having none of it.
Best overall advice I can offer is just to roll with it and recognize that bring a toddler will make the experiences revolve around them. That said, as a family we've loved and all of our kids have cruised before even hitting a year old.