Does your head tube have different sized bearing seats top and bottom?
The fork you link to has a tapered steerer (you can see the taper fairly clearly on one of the enlarged pictures). If you buy this headset, you'll need to find another Q Pro fork, or a fork of similar design.
It seems that the Q Pro used an unusual combination of headset parts, with a 1.75" lower press fit, and a 34mm upper, with a 1 5/16" lower steerer diameter tapering to 1" at the top. Obviously you can measure your frame to see if it corresponds.
This page (in French) shows a Q Pro frame and fork, and lists the relevant dimensions:
It appears that the 2002 TREK 5900 used the same headset. It would make sense to approach a Trek dealer if you have a good one nearby. It should be possible to use adapters to fit a more common fork.
Calmes dans le demi-jour
Que les branches hautes font,
Pénétrons bien notre amour
De ce silence profond.