Hi Jessica!
Stroller rental is as simple as 1,2,3 when you arrive at your first Disney theme park for the day. There has never been a time that I've seen Disney not have any strollers available for guests to rent upon their arrival no matter the time. However, I would recommend arriving at the park as soon as possible for you to be sure that you and your little one will be comfortable during your Disney day.
We normally rent a stroller from one of the featured Disney providers (Kingdom Strollers, Orlando Stroller Rental, and Magic Strollers) and have it delivered to our resort or Orlando area hotel. This ensures that we will have a stroller for our entire stay, and having a stroller that can recline when our little one needs a mid-day nap is always helpful. The theme park strollers cannot recline, but they have plenty of room for your little one to be comfortable and enjoy the sights and smells that Disney has to offer.
Also, the strollers from the third party meet all of the size requirements that Disney is now enforcing.
Jessica, have the most magical time at Walt Disney World. If you have more questions about
things to do with your little one, please stop by and visit with us again soon.
Happy planning,
Korliss