You should go here first:
https://tpwd.texas.gov/huntwild/hunt/public/I don't think you can't hunt rabbits and prairie dogs at Caprock Canyon.
You have to find the specific regulations for the property you want to hunt. Just because something is a non-game animal doesn't mean you can kill it on public land. You have to find what's legal game and when the season is open for that property.
TPWD isn't all inclusive for public land in Texas. There's also US Forest Service, US Army Corps of Engineers, US Fish and Wildlife Service and more. You have to find the rules for the place you're going to hunt.
For example, A lot of US Forest Service land lets you hunt feral hogs year round and some TPWD that has seasons and restricted weapons for them.