I have fished the Upper Q a lot in the past 5 years. It is one of the most beautiful river I have ever experienced. This past year alone we boated 7 fish that were over 25 lbs. One of the best things about this river is how quick it comes back into shape. Of the three majors that I fish (hoh, queets, upper quinault) the upper quinault is fishable way more than the other two.

As far as the lower quinault, if Robbin Rhoades is still guiding he is a pretty good bet. If he is not I would have to second the post about Letty Potter.

If you are looking for numbers December and January are a good bet. You might even tie into a nice king or coho in December. If you are looking for size, late February through the closure in April is good to great. I have personally caught more big fish out of the hoh than the upper Q, but the upper Q is by far fishable longer.
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"Many go fishing all their lives without knowing that it is not fish they are after." - Henry David Thoreau