Started learning QuakeC a couple days ago, and have been doing pretty simple stuff just to get the hang of things. When I say simple things, I mean VERY simple stuff like:

if(self.key_bind4 == TRUE)
{
self.walkframe = 109; //play an animation from the mdl
}

I wanted to know if there was some way for me to add a damaging hitbox to the player when they hit this button and the animation plays. An example would be an animation of the player swinging a bat or something, and a hitbox being created where the bat physically is. I'd appreciate any help! 

Quake is a much more abstract game than that. The hitboxes don't rotate, and the physics is modelling everything as a particle (at best). The Quake axe just traces a straight line a short way down the crosshair line, like a bullet with a 4 foot range. This isn't through lack of imagination or because it produced better gameplay - it's simply the kind of thing the engine is built to do.

With the technical limits set aside, I think there is an argument that first person games favour melee weapons that produce a precise stab of damage rather than a long swing. The problem is the player can freely move their camera between frames of a swing, If they move in the direction of the swing, they might stretch it out further than you intended, either leaving gaps the swing does no damage on, or dealing damage in a huge area of effect. On the other hand if they rotate against the direction of swing, they might inadvertently cause a whiff, or stack multiple hits in one spot.