This sounds like a fairly recent slang term, doesn't it? I can so easily see some Hollywood bigwig b.s.ing some lowly scriptwriter: "Yeah, babe, your script's hot, JLo loves it, and Steven wants to direct, but there's a bidding war, so we gotta keep it on the QT or Warner's may pull out of the deal..." But actually, the phrase is old as the hills.

The "Facts on File Encyclopedia of Word and Phrase Origins" says that this phrase first appears in a British ballad clear back in 1870--the line from the ballad goes: "Whatever I tell you is on the QT", which is pretty much exactly the way it's used today. It was pretty clearly engineered to simply slash the spelling down to the first and last letters of the word "quiet". Hey, it's worked for hip-hop artists for the last 20 years, so I guess we can let 19th-century balladeers get in on the act, too.

Source: http://www.quinion.com/words/qa/qa-ont2.htm