Got the "original" Death from Neil Gaiman's The Sandman yesterday, another DC Direct action figure. This Death has no hat (which was molded to the head on the other figure and couldn't be removed) but did have a rolled umbrella, as per the illustration previously posted. Rather than simply re-running that image, here is a panel showing her saying one of my favorite quotes from 'Facade' in Dream Country.
Terry Pratchett's Death (who is the more traditional skeleton in robes with scythe) says a line very similar in one of the Discworld novels. Pratchett and Gaiman collaborated on the novel Good Omens, and seem to enjoy referencing each other's work now and then. Who wrote it first? Don't know; can't say; daren't speculate.
Thanks again to Tom at Z's Toys for hunting her down for me.