Hello Philip,
I'm so excited to know you'll be spending a magical Christmas with your darling little princess at Walt Disney World Resort, it's sure to be practically perfect in every way!
You are very wise indeed to be considering hiring a buggy (or stroller as our American hosts refer to them) during your holiday as small children do tire easily with all the extra walking and in my experience even a big, quite grown-up child will gladly revert to being pushed around in a buggy! Another big bonus is that a stroller also doubles as great storage for sundries like water, sun cream, purchases and so on...
Each Disney Theme Park has conveniently placed
Stroller Rental locations where it's possible to hire strollers daily or indeed for length of stay. In addition Guests also have the option to hire strollers from private companies; all details are listed within my previous link.
If I can help sprinkle any extra pixie dust onto your Walt Disney World Resort Christmas holiday plans please pop back to ask me another question.
Have a great Disney day.
~ Jane