Hello Tony and welcome to the Disney Parks Moms Panel!
Strollers are an essential component of a Walt Disney World vacation when traveling with little ones. I can remember one very long walk through the
Epcot parking lot carrying our rather large five-year-old grandson when we wished we had brought a stroller along!
The most important thing when planning your stroller strategy is to know and understand
Disney's rules. For a stroller to be "Disney approved," it may not be any larger than 31″ (79cm) wide and 52″ (132cm) long. If the child conveyance vehicle you describe is an actual stroller and not a wagon (either push or pull) you should be ok.
While Disney doesn't maintain a list of approved strollers, they do have a list of preferred stroller rental companies if you decide to rent instead of bringing your along:
Magic Strollers: (866) 866-6177
Orlando Stroller Rentals: (800) 281-0884
Kingdom Strollers: (407) 271-5301
Of course, if you would rather, you can always
rent a stroller at the parks. I hope this helps with your planning.
See ya real soon,
Anne