A few years ago our German Shephard killed a large cottenmouth in our backyard - it had wondered into our mulch filled playground set where our kids were playing. We couldn't tell if he was bitten (the dog, not the snake - the snake was bitten in half), so we rushed him (the dog, it was clearly too late for the snake) to the 24hr Vet. That's when we got a quick and valuable lesson about dogs and snakes.
It's not like people where the antivenin works everytime. It doesn't always work and I understand it can have deadly side-effects as well - plus it's ridiculously expensive. Several hundred a vial and a 120lb. dog could take as many as three, perhaps even four vials.
We stayed at the vet for a couple hours, but it luckily it turned out the dog wasn't bitten.
I had a Lab that got popped in the jaw by a Copperhead. Swelling started pretty quick. WE took her to the vet right then. She was home that night but swollen pretty bad. She took a hit for me. I was a kid then. Dog made it through OK.