We took our dd on her first trip to WDW last month. She was 13 months old at the time. We brought our own stroller, a Graco CitiLite which is lightweight and folds up pretty flat. She was very comfortable in it and it did recline for her morning and afternoon naps. We did fly to Orlando and gate checked the stroller. I do recommend bringing your own lightweight stroller that reclines so the baby will be comfortable enough to nap in it.
We also brought our own carseat, a Cosco Touriva, which is a very lightweight one that worked well on the airplane and was easier to carry. Installing it on the plane was very simple. We don't use this carseat as our primary carseat at home, but it works very well as a travel carseat.
At the airport we rented a car and used it exclusively as our transportation to the parks even though we stayed on site. We didn't want the hassle of lugging the stroller on and off crowded buses. Folding up and carrying the stroller on the parking lot trams was very easy though. You don't have to fold up strollers on the monorail or on the WDW boats. Since we stayed at Port Orleans Riverside, we made a trip to Downtown Disney on the boat which dd loved!
We used the pack n play Disney provided in our room and dd slept very well in it. Disney does provide a fitted sheet and blanket but we also brought along a spare as well as her favorite crib toys to make her feel more at home.
We rented a highchair and fridge(cheaper than Disney's prices) from A Baby's Best Friend(mentioned above). Both items were waiting for us in the luggage room when we checked in. Bell services delivered them to our room. We were glad we did this!
Dh and I have made 16 trips to WDW before Madelyn was born. Our 17th trip was our first with her. A totally different experience but we had such a good time and so will you!
If you have any questions, feel free to ask away!
BTW, dd favorite "ride" was the parking lot tram!!!!!! Go figure.
