As a parent, you already know that you dont want to have to carry your child around in your arms all day. You couldnt possibly make it through the day! You also cant expect your child to walk all day long. The obvious choice is to have a way to transport your child without wearing you or the child completely out.
Strollers are not only welcome at Disneyland, they are highly recommended. In fact, Disneyland rents strollers for a reasonable fee. Strollers can be rented for less than $10 for the day, and you can get a huge discount on a second stroller if it is needed. The strollers are clean and well-maintained, but they do all look alike. Tie something on the stroller, such as a brightly colored ribbon, to help identify it from all of the other strollers in the park.
Never leave your child unattended in the stroller, and never leave any material items of any value in the stroller either. Even if you bring your own stroller, you should have some easy way to identify it there will be other strollers that look just like it at Disneyland.