Howdy Christine!! What a magical vacation! Disney's Beach Club Villas combined with breakfast at
Chef Mickey's - LOVE IT!!!
There are a couple of items that I would suggest you find out before you make your reservation. 1. What are the hours of Magic Kingdom on the day you will be dining? 2. Will Magic Kingdom offer early Extra Magic Hours on the morning you enjoy breakfast?
Once you know the answers to the questions listed above, you will know how early the buses will be running each morning.
From there, I would give yourself an hour and a half to get to the resort. Disney Cast Members typically suggest you give yourself an hour to get from one location to another. You don't typically need that long but it's better to be safe than sorry, especially when dealing with dining or event reservations. This will give you an hour to get to Magic Kingdom, 15 minutes to take the short walk from Magic Kingdom to Disney's Contemporary Resort and then you should arrive at Chef Mickey's at the perfect time to check-in. If you arrive early, the Contemporary has some great shops or you could walk out and have the opportunity for some amazing photos with Magic Kingdom as the backdrop.
Since you are staying at Beach Club, you might also consider
Cape May Cafe as a dining option when you are making your dining reservations. The food is wonderful and you have the opportunity to meet and greet with some of your favorite Disney Characters dressed in beach attire. It's one of our favorite breakfast buffets.
Thanks so much for your question and please let me know if you need any further information. Have a magical day!