First of all, congratulations on your upcoming arrival!
You will be in good hands traveling
DCL with your little one. When I book a cruise with a baby, I usually splurge for a Verandah stateroom. That way when I need to put the baby down for his nap, or bedtime, I don’t have to sit quietly in a dark room while he sleeps, and I can go sit out on the balcony, have a drink, and read a book!
DCL will provide a pack & play so don’t worry about bringing one - the less you have to carry, the better! You can also request a high chair for the dining rooms. They can also help with purées or appropriate foods assuming your baby will have started on solids by that age. Speaking of dining, when I cruise with a baby I always try to get the main dining because I find the second dining option is just too late for them to stay up. HOWEVER, if you are from the US and traveling to Europe, your baby may not be adjusted to the time zone and stay up later naturally. When I took my 7 month old to Scotland, we kept him on a very late schedule so he didn’t have to adapt so much to the time change and then again when we returned home, and this also made it easier for us to go out to dinner and still get the baby to bed before he got too tired. So if that is the case with you, you may want to opt for second seating (giving you more time in each port during the day) and let your baby stick to a later schedule for the duration of your trip overseas.
With the nursery onboard, you can only book a certain number of hours online before the cruise, and the rest you can book once you board. If you want to plan any adults-only dinners, spa, etc, make sure you coordinate to get those hours in at the nursery as well.
Beyond that, there’s not too much to worry about while on the ship! If you will be bottle feeding, bring your bottles and a travel size bottle of dish soap so you can clean them in the sink between uses. Diaper prices will be much higher than at home, so bring all the diapers you think you will need (and then by the end of your trip you will have extra room in your bag for souvenirs). Normally I wouldn’t bring my stroller on the ship because it can be crowded and we never have far to walk, but going to Europe you will definitely want one for the port days. They can store your stroller until you are ready to use it so it doesn’t crowd up your stateroom.
I can recommend my favorite baby travel products if you are curious but since it’s not DCL specific I won’t go on for now. If you have any specific questions let me know!