You can't get to DTD from the theme parks directly; however, there is an easy way around this.
Take the monorail (or walkway) to the Contemporary. Or take the monorail to GF or the Polynesian.
From the resorts, just hop on their bus to DTD and enjoy. It's about 20 minutes or so once you get on the bus. Many times, there is just one shared bus for GF, Poly, and Contemporary, which will add to the time (I believe GF is the last stop when they are sharing a bus).
If you're looking for a midday break with good shopping, and DTD seems a bit far, maybe consider going to the Boardwalk. There is great shopping and dining, and the scenery is beautiful. You can also walk to the Yacht & Beach Clubs, or even to Epcot. Just get right on the Boardwalk bus from MK. I think it's about 10-15 minutes, and much more direct than getting to DTD.