Y'all need to be at the Contemporary Resort by 7:00 am to check in for the breakfast at Chef Mickey's. (Great thing to do, methinks. We did it with our group once, and the food was really good I thought, and the kids loved the characters.) Since I don't know what time the Magic Kingdom opens on the day you are going to Chef Mickey's, I really can't advise.
You should check to get the starting time for the bus to the Magic Kingdom. Once there, you can walk to the Contemporary or take the monorail, but you have to be sure the bus will be running from your resort to get there in time.
If it were me, and I had any doubt about making it in time, I'd simply take a taxi from my resort to the Contemporary. Just stop at guest services in the lobby and have them call you a taxi.
Enjoy.