Well, originally "Ditzy Doo" was just a name they'd tossed out in dialogue without attaching a pony to it, and they were thinking that if they needed to assign it later, they'd give it to the wall-eyed pegasus - but then the Internet loved "Derpy", and Lauren said "she can be Derpy if everyone likes" and it caught on with the writers and thus, Derpy.

The mail carrier thing is 100% fanon, though. Although I guess there's that scene in Pinkie Keen, where she dropped something on Twilight - but that was actually better than this because it was clearly a clutzy moment (depth perception is hard when your eyes are facing opposite directions!!) and she obviously felt awkward and embarrassed about it.

It's like she took a few whacks to the head between seasons or something.