michael,
Well, yes and no, with no special significance applied to the order of those two words.
The dollar will do whatever the market makes it do. I don't think the Fed will be messing directly with the dollar (by trading it against other currencies), but that doesn't mean they can't do that at some later date if they want to (through negotiation with our Treasury department). The Fed is only legally bound to do what they can do through monetary policy to try and maintain full employment and low inflation. The only other tool available to our government is fiscal policy, and that is up to the legislative branch of government, which is a wee bit dysfunctional.
QE will do whatever the Fed makes it do between the Fed, the Treasury, and the banks. They can reduce it or increase it or change its partitioning between Treasuries and MBSs at any time. Once the QE is on the banks' balance sheet, whatever happens to that is up to the banks. So far, much of that has been to improve their liquidity (stayed in their vaults). But that's a good thing because it's deleveraging the banks, therefore making it harder for them to fail. Because it stays at the bank, and isn't circulated, the velocity of money decreases. The net result is that they aren't really printing money.
Well, the dollar goes up because other countries have more faith in our currency than they have in other currencies. That has been our history but wont be forever. Probably the Chinese currency will be the next great currency. Other countries (say Japan) are messing with their currency, but we aren't messing with ours right now (at least that I know of). Japan is a special country with lots of people and advanced industry and few natural resources trapped on a string of islands, and this gives them unique and special problems. It seems to me that the only thing Japan can do to increase their physical wealth is to increase intellectual property (make things out of little but ideas) and that's very difficult to do because the rest of the world is getting smarter and smarter.