Hi, Amber!
Great question!
You'll be pleased to know that the movie theater at Downtown Disney is the
AMC Downtown Disney 24. Not only will you find the very same movies here that you'd find at any other AMC Theater, but you'll also find some really cool features that you won't find in your typical local movie theater. (Personally, I can't wait to head back to Fork & Screen Dine-In Theaters, which include a personal call button and seat-side service of burgers, sandwiches and even cocktails!)
As such, if a movie is opening on the day of your arrival in Walt Disney World, then head on over to AMC Downtown Disney 24. You'll be thrilled with the venue, and your daughter will be thrilled that she doesn't have to skip the opening of a great flick because you've just arrived in WDW. WIn-win!
Send more questions as you think of them, Amber; we love to help!