The decline of the dollar under QE has been nothing when compared with its decline from 2002 to 2008.
Between high water marks in early 2002 and a low beneath 70 in March 2008 the trade weighted dollar sank a whopping 36% in just six short years, 6 times more than the 6% it fell since TARP passed on October 3, 2008 and QE began in late November 2008 until now.
Say what you will about QE, but it's just dumb to blame it for a decline of the dollar.
The dollar was already dead! The dollar declined 36% during the wars in Iraq and Afghanistan. Overall the dollar is down 6% since the emergency measures of 2008, but is recovering somewhat.