Just check to make sure your stroller isn't too big:
Are there any personal items I should not bring with me into the theme parks?
Items that you may not bring into the theme parks include but are not limited to:
Items with wheels, such as:
Wagons
Skateboards
Scooters
Inline skates
Shoes with built-in wheels
Two-wheeled or three-wheeled conveyances
Strollers larger than 36" x 52" (92 x 132 cm)
Suitcases, coolers or backpacks with or without wheels larger than 24" (61 cm) long x 15" (38 cm) wide x 18" (46 cm) high. (Coolers required for medication may be stored in a locker or at Guest Relations.)
Any trailer-like object that is pushed or towed by an
ECV wheelchair or stroller
Alcoholic beverages
Weapons of any kind
Folding chairs
Glass containers (excluding baby food jars and perfume bottles)
Pets (unless they are service animals)
In Disney's Animal Kingdom theme Park (for the safety of the wildlife), balloons, straws and drink lids are not permitted.