I just wanted to add, unless something has changed, you'll want to bring your own stroller if you need one for your infant. Not sure how old, but when I went w/ my two year old and 4 month old, I called ahead to see if the WDW rental strollers would work for my 4 month old. I was told that the double strollers would be fine. I discovered that they were not after I had already rented one. There was no way the baby could be in that stroller!
I ended up getting two singles - one of them was more designed for infants. After using it for a few days we purchased one of the red and black umbrella strollers in the resort gift shop. It's pricey (around $50) but a great stroller. The height is perfect, unlike most umbrella strollers I don't end up hunched over or kicking the bottom crossbar when I walk.
Sorry for the long response, but I wish I had known about the WDW rental strollers ahead of time, I had quite a moment when I realized that the double stroller I had just paid quite a bit for was completely useless!