It’s quite a common phrase in the UK, meaning ‘task complete’.
“Have you finished compiling those statistics?”
“Done and dusted!”
I have nothing on date, but I’m wondering whether it comes from domestic servants’ parlance.
Hmm, nothing in OED, which slightly surprised me. It’s been current for years, and, though memory is often treacherous, I’m pretty sure it was around in the 50s/60s.
182,000 googlits. Obviously it’s alive and well. From a quick lookover, they seem to be mainly from British and Australian sites.