Hiya, Dave! Thanks for your question.
Walt Disney World is great when it comes to
transportation options, and there are ways to get from
Disney's Old Key West Resort to
Disney's Contemporary Resort. It's just a quick trip between your wake-up call and those Mickey waffles.
Disney bus transportation begins running about an hour before the theme parks open, so whether or not the bus will be an option depends upon your
dining reservation time at
Chef Mickey's. If your reservation isn't super early, you'll take the bus from your resort to
Magic Kingdom Park, and from there, you can either take the short walk over to the Contemporary Resort or hop on the resort monorail for a quick ride over.
If you're using the bus, I'd say give yourself an hour between the time you leave Old Key West and your reservation time. The trip itself isn't that long at all, but you may have to wait a few minutes for the bus, and it's better to give yourself a little breathing room.
Another option that may work if your reservation is super early is the
Disney Minnie Van Service. Minnie Vans operate like a rideshare service through the Lyft app, and this service begins running at 6:30 AM. It's not only perfect for an early morning breakfast reservation, but it also lets you sleep in a few minutes longer. You can probably shave your travel time down to 30 to 45 minutes using this service.
Enjoy a fabulous vacation, Dave!
Anna