That's a great question. I'm a huge fan of the My Disney Experience app and have used it many times (not just at Walt Disney World, but also at home as I've been finalizing my vacation plans).
Unfortunately, I don't think the My Disney Experience app works on the BlackBerry platform at this time. Sorry!
Don't worry, I've got an idea that might help you get access to the My Disney Experience app!
If you have an iPad or iPod that's running iOS 4.3 or later, then you can run My Disney Experience on either of those devices instead! Similarly, if you have an Android-based tablet (running version 2.3 or higher), then you can use that as well.
My Disney Experience kiosks have been setup all around the Walt Disney World theme parks. So, if you're not able to bring a mobile device that can run the My Disney Experience app, you can just swing by one of the kiosks and make any necessary edits or changes to your vacation plans.