Hi, Ariadna!
Welcome aboard!
We sailed with a two-year-old on our very first Disney Cruise. The best advice I can give is to take lots and lots of pictures! We love looking back at how little our daughter was on our first DCL vacation, and how magical everything was to her. (It still is, even though she's eleven now!)
Also, make sure to take advantage of the wonderful Youth Services on the ship, so you can relax and enjoy some "grown-up time" on your vacation. For the littlest cruisers, there's
It's A Small World Nursery. The nursery requires reservations, and has a minimal fee. For young guests ages 3-12, the
Oceaneer Club is the place to be! Fun Youth Counselors entertain and care for the kids while the grownups have a quiet dinner or enjoy the nightclubs and lounges. My kids love the Youth Clubs!
If you'd like to have bed rails on your daughter's bed, simply call and have it noted on your cruise reservation, or speak with your stateroom host/hostess on your first afternoon onboard. They will be happy to take care of that for you! As far as a stroller, they encourage guests to bring their own. The best options are lightweight, foldable strollers. That being said, there's a very limited supply of strollers onboard, which are only available on a first-come, first-served basis. We picked up a lightweight umbrella stroller for our cruise (princess motif, even!) for less than twenty dollars, and it easily folded and stored in our stateroom. No need for a big bulky stroller, just a small one will do fine!
I hope this helps with your planning! Wishing you a most magical vacation with Captain Mickey and his crew! - Diane W.