Yes, as the PP mentioned, it's a short walk to MK from Chef Mickey's (we are fast walkers and can do it in about 5 minutes. The walk is nice (except where you cross the street, it can be a little busy sometimes, don't worry there is a stop light).
However, if it's your 9 year old daughter's first trip, a ride on the Monorail is way more exciting than walking. Take the extra 15 minutes, she will love it. For my kids, taking the Monorail is better than some of the rides at Disney.
If you are staying in a Monorail resort, walk to MK and take the monorail back.
Have a great time. I'm excited for you and your daughter!