Hi, Sheryl!
Yes, you can bring unopened water bottles in their original containers on board a Disney ship. However, you'll need to pack them in your checked or carry-on luggage -- which makes it kind of cumbersome as you make your way to and onto the ship.
Instead, I recommend ordering a case of water bottles from the
Gifts & Amenities Page on the DisneyCruise.com Planning Center. You may pay a little more, but it's so worth it not to have to lug that case to and through the terminal and possibly on the ship until your stateroom is ready. Your water bottles could be waiting on you in your stateroom when you arrive.
Another idea is to purchase an insulated reusable water bottle for each member of your family. There is chilled water (and ice) available at the 24-hour beverage stations on the pool decks of each ship. The water is purified (and free!), and my kids enjoyed filling up their water bottles to carry around the ship or at ports of call.
I hope this helps you plan. Let me know if you think of more questions before you sail next year. Have a wonderful day and a magical vacation.
Bon voyage,
Andi