Apologies for resurrecting an old thread.
One thing that I always have with me when traveling with dogs is a muzzle. Yes I know how to improvise one and have done so, but a nylon muzzle like a Miki muzzle is cheap, easy to carry, more effective, and more comfortable for the dog.
If your dog is injured, a muzzle can literally be a life saver for the dog. In a disaster or rescue situation it is more likely for your dog to be allowed in a transport vehicle or shelter if he can be securely muzzled. Some agencies/pilots require that we muzzle our SAR dogs for transport. These are the same agencies/pilots that will be providing transport in a disaster or rescue.
Muzzles aren't EDC, but they go wherever the dogs go. Plus backups in the disaster kit and BOBs.