Hi Shannon!
How exciting that your Disney Cruise Line countdown is underway! Disney Cruise Line does have a limited number of complementary strollers available on a first-come, first-served basis. On my most recent sailing (just a few months ago) the strollers were Peg Perego-brand, full-sized models. These are, of course, always subject to change. While the strollers are complimentary, you will need to leave a refundable deposit via your Key to the World card.
If you are headed to Castaway Cay, you won't need to take the stroller, as there are plenty of both strollers and wagons available free of charge at Scuttle's Cove Tram Stop and at Pelican Point Tram Stop. These strollers and wagons do not require a deposit and are there for anyone to use as they enjoy the island.
If you chose to use a complimentary stroller on board, I do recommend that you go to the Guest Services desk on Deck 3 as soon as you board to reserve one. If, however, you chose to bring your own, I have found that a compact umbrella-style stroller fits nicely under the bed.
I recommend that you visit
Traveling with Little Ones for some additional helpful information. Once on board, be sure to consider Jack Jack's Incredible Diaper Dash, where the tiniest of passengers gear up for an exciting (and hilarious) race while hundreds of passengers cheer them on. To this day, it is one of the highlights of our trips with Disney Cruise Line!
Bon voyage!