Hi Shannon,
Thank you for your question and it is a tough one to answer.
In theory, Disney dining knows you are coming to Chef Mickey's at 7:20 am. This information is usually coordinated with Disney transportation to make sure you have a way to get to your reservations. However, this sometimes the pixie dust clogs up the plan.
Disney transportation begins running to the parks at one hour prior to the park opening. If Magic Kingdom is going to open at 7:00 am, you will be fine to hop on a bus and then walk to the Contemporary. You can confirm Magic Kingdom's open on the
calendar or at your resort with the time guides.
You should talk to concierge about your early start. The cast member will be able to offer you guidance on transportation and can help coordinate a taxi if you need it.
Wishing you a magical vacation!
Beth