We went with our 13 month old last cruise. A little different in age, but we had just started walking and some other big milestones...
-Incase you didn't know,
DCL will provide a diaper genie to your room. If you child has an allergies/sensitivities; bring your own sheet for the PnP.
3rd on the small stroller. Don't feel bad about using it throughout the ship, there will be plenty. You can also rent/borrow one from DCL once on ship if you choose. They are nice CityMini's
-No Diapers in the pools or aquazones, only in the splash area. My daughter loved that anyway
-Don't feel like you have to do MDR everynight. It does take a long time, and if your LO is crashing, ask to have the rest of your dinner sent to your room OR eat up in Cabanas (its really nice and quiet) OR take to nursery then go back to MDR. Dinner is a long ordeal.
-If you are not going with a big group, call DCL and request a table in the MDR alone! This helps it go faster and helps (a lot!)
-Book your nursery times early (now) if you want to use them. They are great.
-Like others said, try and stay on a normal schedule. Naps when needed, many things on the ship are repeated. Characters are all the time. Don't overdo it
-Look for the toddler events, they are great fun. There is a toddler meeting time, diaper dash and couple others. Good times for the little ones and memorable
-bring a sponge or towel,covered in liquid soap and dried, then cut into pieces to wash bottles and other items. Makes washing in the stateroom easier
-If you need to save luggage, use the baby item delivery service. Prices are a little more then you would pay, but worth not taking all the diapers/wipes/milk/snacks/foods etc.
-DCL will make any veggie (maybe food?) pureed for babies if you ask
-take a small sand toy for the beach at CC
-wagons are available once you get off the ship at CC on the left side. Just have to get them early on, but keeps from bringing stroller
If I think of any more I will post. 9 months will be a great time (hopefully before walking). Once they are on the move, it is rough! Have a great time!