There are two stages in the story where dogs are mentioned. Firstly, when John has reached the City of the Gods, he sees a dog who obviously begins to hunt John: "he looked at me as if I were meat." As John walks towards some towers on a god-road, he sees that there was a whole pack of dogs with the first dog, obviously waiting to catch and eat him. John escapes from them by finding a tower with a door that he could open and then shut against the dogs, who chose that moment to attack. The door was strong and made of metal, so they were not able to get through.
Towards the end of the story John says of his return journey that he had two fight off the dogs twice to go back home, but he says nothing more than this, so we are left to imagine how he escaped.