Correct me if I'm wrong, but the ECB hasn't done any QE yet (although only because the Germans are against it, after what happened last time they tried it!).
The problem the eurozone faces IMHO is that they need more money for bailouts than they can realistically raise. And even if they do raise the money, they're probably only kicking the can down the road.
And they need to be careful, or what they're doing could lead even to wars! If the eurozone borrow 100 billion euros from China and then tell them in a couple of years' time that they'll need to take a 50% haircut, I doubt the news will go down well!
Jeff