Hello there John! Welcome to planDisney, we're so glad you're here!
Strollers are available for Guests to rent during their visit at all of the theme parks as well as
Disney Springs. You can even purchase a Length of Stay rental ticket if you'd like to rent for multiple days. The strollers that are available for rent at Walt Disney World Resort do not have a ton of storage space. There is usually a place you could store a beverage or reusable water bottle on the back of the stroller, but it does not have the storage underneath like other strollers do. Depending on how big your little Mouseketeer is, you could potentially put a small cooler bag next to them or down near their feet, but it may be a tight squeeze!
My recommendation would be to bring a backpack that you could store your small cooler in, or you could even checkout the
locker rentals on-site at each theme park. Each theme park has a few different size options to choose from, and there is a one-time charge for the day. It can be a great place to store your personal items you do not want to carry around, or store any souvenirs you purchase throughout the day as well!
Another option you may want to explore is a
local stroller rental company such as ScooterBug. They have different stroller options for you to choose from, and they'll even deliver to your
Disney Resorts Collection Hotel! If you're ever in need of any essentials for your little ones or a quiet place to change a diaper, I highly recommend visiting the
Baby Care Centers located in each theme park. It was such a nice break for my kids when they were younger to get out of the parks for a bit and have some quiet time. The Cast Members are wonderful, and they make sure you have everything you need!
I hope this information helps answer your question, John! If I can answer any other questions for your upcoming trip to the "Most Magical Place on Earth,"
please come back and ask!
Have a magical day!
Melissa