Put together a resume and acting history for your child. If she's had any sort of experience—whether it was acting camp, school plays, commercials or modeling—it should be mentioned. Take headshots and include those headshots with the resume for the casting director. Make sure the photographs are kept up to date, as children's appearances change very quickly.
Find auditions for Disney shows and movies. Disneyauditions.com collects information about all of the casting calls on one website, letting you know where you need to be and what you need to bring. Regularly check this website to stay up to date on what's casting in your area and whether or not your child fits the bill for what the company is looking for.
Attend as many auditions and casting calls with your child as you can. Remember that you'll likely have to try several times before landing a role, due to the competition for the few spots available in Disney productions. You and your child need to be professional and mature, and you need to practice line memorization and quick reading for scripts in order to be as prepared as possible when it comes time to perform for the casting directors.