This addon adds a command to check whether you've completed a given quest yet or not.
Note that the table of completed quests is only refreshed after a logout/login, so if you just turned in a quest it won't show up as completed until after a logout.
To get the ID of a quest, search for it on wowhead.com and copy the number at the end of the URL
Commands:
/qq xxxxx - See if you've completed the quest with ID xxxxx
/qq [Quest Link] - See if you've completed the given quest
/qq v[ersion] - Show addon version
/qq help - Show command help