post a link to a video or explain what your after a bit better so we can help you. personally i havent played quake in decades so i dont remember much of it.
Edit:
so i just downloaded and played abit of quake and its movement is a basic first person setup wasd are forward/back and strafing, the mouse is rotation yaw, and the arrow keys are forward back & rotation. if i were you id look at the first person template character and how thats setup. ill include a picture below of some of the pertinent script for forward back movement and rotation. the only other thing about quake thats different is the persistence of movement, basically whne you release the walk forward button the walking doesnt immediately stop but continues on for a sec.