In Pathway, a dog is a "side" hero which can't be selected in the expedition screen. You can add this animal to your party when one of your members dies - you have a chance of meeting this animal when you are traveling on the world map. A dog can have a different model or slightly different stats, however, they will be similar.
A dog is a rather powerful hero. It has a great movement range. Its bite attack, which costs Bravery points, can cause Bleed effect. However, the animal doesn't have any armor nor additional skills. It also can't use weapons or items. Important: when your dog dies, it usually means that the expedition is over.
You won't always find a dog after you lose some of your characters. The animal usually appears when you lose one out of the two characters in your party.