I'm a super noob at Fox, having only played him for a week now against scrubs, but maybe I can share my DD thoughts with He Man, beginner to beginner. The rest of you, please correct me now while I'm still learning so much.
Since I'm not as experienced, I'm always prepared to WD backwards out of my DD. This doesn't mean that I always do it, but that's the option I constantly remind myself of. If the opponent gets a bit aggro with an approach, you can do the whole WD back and forth and get a nair/grab/etc thing Fox does so well.
Otherwise when DDing, I'm thinking about how I can make my opponent miss. WD backwards is one way of doing this. Another thing I'll do is DD, break out into a full dash, and then WD straight down/backwards to stop the momentum. With that, sometimes I can trick the opponent into thinking I'm going straight at them, only to break the momentum as close as possible without getting hit, and follow up with whatever approach works best.
This last bit I'm shaky on its viability, so maybe some critique. If I really need to get some field position, I'll be almost stupid with my DD. For example, I'll be DDing pretty close so that I'm just barely outside of attack range. Then I try to use the shine to intercept their grab/attack to establish some position quickly. I don't try this against some characters like Marth though.
So that's my DD thought process as a very young Fox. Anyone want to point out any problems in my logic?