Consider your stroller options.
Rental strollers* cost $15 a day ($31 for a double) and certainly don't look like the most comfortable set of wheels. The main fault with the rentals is that they do not adjust, which means no laying flat for naps. Though a stroller is a big thing to lug around, having your child comfortable at the park — they will spend most of the time with their tushes in the stroller anyway whether they're walking yet or not — will make everything run a little smoother.
*If you choose to use one of Disney's rental strollers, prepay for the entire length of your stay on your first day at a discount ($13 per day for a single, $27 for a double).