Killing a wolf might be an offense that would get you arrested, depending on the regulations in that particular area.

On the other hand, I'd keep the dog on a leash so he doesn't run off and get into confrontations with wolves or bears or cougars, any of which might enjoy a dog meat dinner. Having the firearm will do no good if the dog is out of sight and/or range.

You might also want to consult with your USFS supervisors to be sure it's OK to have your dog and your firearm with you while on the job. They may have a liability issue with either or both.