Strollers are permitted at Disneyland, and can be rented for a reasonable fee. Tie something brightly colored to the stroller to distinguish it from other strollers, and never leave any valuable items in the stroller.
As a parent, you already know that you don't want to be carrying your child around all day. You're not going to make it through the day!
You can't also expect your child to walk all day.
The obvious choice is to have a way to transport your child that does not exhaust you or the child.
Strollers are not only permitted, but also highly recommended at Disneyland. Disneyland, in fact, rents strollers for a reasonable fee. Strollers can be rented for less than $10 per day, and you can get a significant discount on a second stroller if necessary. The strollers are clean and well-kept, but they all look the same. Tie something brightly colored to the stroller to help distinguish it from the other strollers in the park.
Never leave your child unattended in the stroller, and never leave any valuable items in the stroller. Even if you bring your own stroller, you should be able to easily identify it because there will be other strollers that look exactly like it at Disneyland.