CTRL+D in Notepad++ just means "Duplicate current line".
I don't believe there's an equivalent in DW.
Perhaps use Autohotkey (or alike) to create a macro that moves to the start of the line, then selects to the end of the line, then inserts a blank line below, and then inserts your copied line.
Then bind that to CTRL+D (or whatever).
Also, you probably can create a macro like this directly in DW using its "Commands" to do the automation.
If you get stuck writing your macro/script, come back with any questions relating to that and create a new question here (but please don't come back expecting us to write it for you ;) ).