Which ship are you going on?
Night nursery is brilliant. Worked perfectly for our 9mo last year as we just rocked him to sleep in the cabin and walked him over asleep on our arms. Had evening free to ourself!
On the bigger ships (Iona, Arvia) they have baby sensory type sessions quite a few mornings, great with a little, just check the schedule. Under 2 there's no daytime childcare but there is a nursery with lots of toys to play with. And just loads of things to see and do to keep them entertained just around the ship.
5-5.45 every day they have "children's tea" in the buffet - just for kids and their families, lots of kiddy friendly food. Overall the food was brilliant for weaning as we could just let him try loads of things and just see what he liked.
Definitely request the baby bath and you can also request a cot if you don't want to trek one with you (we took one when we went from Southampton, didn't take it when we went from Valletta and had to fly out).
Check the excursions - we were obviously limited in what we could do with a baby but still found quite a few options that worked.
Most of the pools are supposed to be kid free but all the family friendly ships have at least one or two pools that are ok for babies / kids.
Take laundry stuff with you - there are laundries you can use and with a baby it's great to know you don't have to take a million vests etc just in case.