You have two options to get from A to D airside: you can use skylink, which takes about 5-10 mins. You can also walk, but it takes a LONG time... the DFW terminals are spread out, and terminal D is more so than the older terminals.
They used to have a bus that ran between terminals, it operated from the curb on the departure level. That is obviously not inside security, and I'm not 100% certain it operates.