We had a 2 year old with us for our breakfast at CM. We took a Disney bus to MK and hopped on the Monorail. (or you could walk, but I would bring a stroller). People have said it is about a 5 minute walk, but it looked like it would be longer to us (plus my 70 something Mother in law was with us and she didn't want to walk it), so we walked to the monorail and rode to the Contemporary. If you have to wait on a monorail, it could take you longer to ride than to walk.
We never drove anywhere when we were there in early Dec. (They may even have a limit on the amount of time you can park in the resort lots, so if you wanted to go to MK after dinner, you would have to drive back to AKL and take Disney transporation at that point, or go park at the Transporation center and take the monorail to the park) We took Disney buses everywhere and if we got somewhere late, it was because we didn't get to the bus stop at the time we had planned. It happened, and we were a little late to a few ADR's, but we never waited for a table more than 5 minutes. We were generally seated right away.
Have a great trip.