Hi Anita,
The stroller rental service at Walt Disney World is top notch. Not only is it super convenient, but it's my opinion that their strollers are so much easier to maneuver around the crowds than most store-bought ones. Even though I own a really nice stroller for my children, I leave it at home when we go on our Disney vacations.
As far as your question goes, if you rent one of the single strollers, your little girl should have no problem fitting into one of those. Plus, the single strollers have two drink carriers, a pouch on the back for some of your stuff, and a rain shield on top.
When I use this service, I opt for the length of stay rental because it's the best value. No matter which pricing option you choose, another neat thing is that if you plan to visit more than one theme park in a given day, you can drop off your stroller as you leave the first theme park and get a new one when you arrive at your next theme park. Just keep your receipt and you'll be all set.
Here's a little tip from your buddy Derek:
When you park your stroller outside of an attraction or show, there's a chance that it might not be where you left it by the time you come back out. The cast members do an awesome job of organizing the stroller parking areas, which means that they might relocate yours to keep the area tidy as guests come and go. It should still remain in the same general vicinity, but I like to tie a ribbon on our stroller's handle so we can easily spot it in the crowd.
I hope that helps! If you should have any additional questions, please feel free to write back and I'll be happy to help in any way that I can.
Best regards,
Derek