You certainly have a VERY refined looking Timex dress watch there and I've never seen that particular style.
I think those Q's appeared on Timex quartz watches from around 1975 until the late 1980's. The earlier Q's had gear trains that were "driven" by balance wheels which were themselves electromagnetically powered AND regulated by a quartz crystal oscillator circuit (was it the calibre 875 that used this approach?). The later Q's dispensed with the balance wheels and just used a solenoid "pulse motor" to advance the movement's gear train and, consequently, are much thinner.
In any event, it is VERY difficult to give any sort of precise figure for how much one could sell his watch for since there are so many factors involved that influence demand. However, being somewhat rare, in cosmetically good condition, running, and having some original paperwork and packaging with it tends to increase the amount one can get for a watch.