I'm not sure if it's technically correct, but it is a thing that could be said. It sounds a bit old-fashioned, so I wonder where you saw it. Have you heard the phrase, "Well, that's that"? It means that something has been finished or decided. Your sentence is kind of similar to "that's that," but with "that" replaced with "this project" and followed by "done and dusted." Here, the word "That" refers to whatever just happened, and the speaker is defining "that" to be the same as "this project done and dusted," or in other words, saying, "the completion of this project is a thing that just happened." I hope it makes more sense now. I wouldn't copy this usage, if I were you, but it's not wrong.

The correct phrasing would be "this project's done and dusted" or "this project is done and dusted".