Do We Have To Expect a Weak Dollar?

I would say yes.
In the short term there is a support at 1.35/1.36.
In the longer term, this impulse to the upside could send prices to retest 1.47 (but let's see how the pullback develops first)
More in general, I believe that president-elect Obama policy will bring a weak dollar. Too much debt, deficits, government intervention, quantitative easing in the long term mean a weak currency. It is possible, however, that as the US will be the first country to recover and to raise interest rates, in that phase we will see a stronger dollar, but I think that weakness is becoming structural.