Hi, Eric!
You're just going to love staying at Disney's Art of Animation Resort! The theming in each one of the 4 sections is incredible!
You've scored a great time for your
Advanced Dining Reservation at Chef Mickey's. Those early Character meals are the only things that will get my family out of bed early during our vacations.
The Disney buses start running very early to transport Guests with early breakfast reservations, so no need to worry. The only thing to keep in mind is that the buses will not travel directly from your Resort to Disney's Contemporary Resort, so you'll need to take a bus to one of the Theme Parks [preferably Magic Kingdom Park] first and then transfer to another bus that will take you to Disney's Contemporary Resort. If you catch a bus to Magic Kingdom Park, you can just follow the walking path right over to the Resort after you get off the bus. It's just about a 5-minute walk. I normally advise allowing 90 minutes of travel time just in case you have to wait for a bus, but this early, you'd likely be safe allowing an hour.
All that being said, the quickest way to get there would be to take a taxi. The cost is typically no more than $20 and if your family is anything like mine, you might want to let them sleep in for that extra hour! The taxi ride is only about 15-minutes from Disney's Art of Animation Resort to the Contemporary.
I hope you enjoy your breakfast with Mickey Mouse and his friends! Please let us know if we can answer any additional questions you have.
Wishing you and your family a Pixie Dusted vacation!
~Jackie