We had a family member who worked for a cruise line when my now 21yo was a toddler and she cruised 4x before she was 4yo.
While it was challenging at times, she had an amazing experience and under the same circumstances (family cruising discount and ability to spend time w/ family member) I would do it over again.
Three of the cruises included my dad (not much help when it comes to child care) and one was just myself, dh, and dd. Our family member was motivated to spend time w/ dd so one trip she took her on excursions to swim w/ dolphins while dh and I were able to do an excursion by ourselves!
In general, dd was (and still is) a night owl. She took schedule changes in stride, did amazing at meals in the MDR, and enjoyed participating in the children's club. One trip I had her completely convinced that they didn't serve french fries in the MDR..and our server was in on it! 🤣 FWIW, we had more issues with other adult passengers assuming she would "act up" at meals than any instances of her doing so.
A few tips...
Bring a lot more diapers and wipes than you think you may need. You don't want to be stuck at sea and run out.
It doesn't take much to amuse little ones. I would figure out a plan for easily accessed basic beach time at ports and bring some sand toys. One of my favorite memories is my dd "watering the beach" for two hours in Cozumel one trip!
Pack favorite snacks, small toys, stuffed friends, blankets, etc. Whatever makes them happy and content!
Use a car seat when traveling on the airplane there (if flying) it made traveling w/ littles SO much easier! ..and when not on transportation, a great infant/toddler carrier to "babywear." Especially convenient when walking around the ship during naptime!