I hunt upland game a lot in rattlesnake territory. In my hunting pack I carry (mostly for the dog but applicable to humans): vet wrap, gauze, tweezers, saline eye wash bottle, benedryl (for snake bite), styptic pencil, peanut butter packet (to administer said benedryl), honey packet, disposable surgical stapler, razor, medical tape, couple of hemostats, mini-roll of duct tape, light nylon muzzle, and some other random stuff. Takes up less room/weight than you would think.
Idea being to deal with the most urgent kind of wounds that either are life threatening and need help RIGHT NOW, or fixable things I can handle right there and finish hunting.
I also did snake aversion training with the dog.
Edit: my hunting guns all have sling swivels but a sling on a upland bird gun is annoying. However, I stuck in a cheap nylon sling in the pack too so if I need to carry out the dog (55lbs) I can body sling the shotgun.
I saw a long time ago an emergency dog harness to strap the dog to your chest. Didn't buy one and can't seem to find it now. Always thought about throwing one of those in.