I'm getting the same problem. I have a battletag, I have logged out of and back into Battle.net numerous times, but I still get the message from oQ in game that Battle.net is down and oQ is therefore disabled. Everything was fine yesterday. Could it have anything to do with the weekly maintenance that Blizz did earlier today?

Update: Intead of logging out/in from the desktop application, I hit the 'back' button from the character screen in WoW, relogged into the WoW log screen, and now everything seems to be working fine both for battle tag and oQ