Hi Kathryn,
Disney and the double stroller! We have
rented the double stroller when my daughters were older because there is a lot of walking at Walt Disney World. Even if we used it in Epcot and Disney's Animal Kingdom, it was worth it. One trip, when they were in 8 and 10, our friend rented a double stroller for her daughter who was five. Both of my girls fit in the double stroller though it was a little tight.
Given your children's sizes, I think you will be fine. If they both cannot fit at the same time, you could rotate them and it not be an issue. You can test it at the front of the park prior to renting the stroller.
The other option is to rent from a stroller company such as Kingdom Strollers, Orlando Stroller Rental or Magic Strollers. You can see if your children could fit in their double stroller.
Wishing you a magical vacation!
Beth