"Mario Draghi said that he would do whatever it takes to save the euro. One way or another this means QE. In which case why did the euro rise after the news that more of the stuff will get printed?"

David Fuller's view Probably because the euro (weekly & daily) was technically short-term oversold and near a previous low, and some people were getting ahead of themselves and betting on a break up of the single currency. However, the euro may not rally all that much.