If you don't want a diaper genie taking up floorspace, Babies r Us has these little blue bags which do an amazing job of masking the odor. We used them with our 16 week old, and never noticed a smell in our cabin.
If you're flying:
I recommend you take your own (full-size) stroller instead of an umbrella stroller. One advantage to bringing your stroller is that at the airport, you get to go in the 'special needs' line at security, which is way shorter than the regular lines. ie, don't put it in checked luggage! Also, the stroller doesn't count towards your carryon allowance (ie you can still have one carryon and one personal item each).
Once you get to the gate and you're boarding, you push it onto the jetway and then fold it up and leave it near the door of the plane. It won't go through the airport's baggage system--they take it down the back steps of the jetway and put it directly into the cargo hold. At the end of your flight (including any connections), they bring it up to the jetway where you pick it up.
On the ship, the benefit is the basket underneath for a diaper bag, plus beach stuff or purchases when you go into port.
We didn't bother with a car seat on the plane--instead we carried her in a Bjorn. Main issue on a plane is turbulence, which IMHO a Bjorn protects them better than a car seat does.
The ship is handicap-accessible, so you won't have any trouble pushing them around in a stroller. In the cabin, we folded it and put it on one side of the bed. And you'll need lots of diapers. Good news is at the end of your cruise you'll have lots of suitcase space where the diapers used to be.
If your baby is on formula, no need to buy or bring distilled water--
DCL water is reverse-osmosis.
but now i know better!!
