I have a friend who walked the PW with her dog, they wild camped the whole way. The dog, a collie, carried two days supply of food in a specially tailored saddle bag restocked at village shops etc. She got the dog used to doing this for a long time before that particular walk. She also said she inspected the dogs paws at lunch time and each evening just to be on the safe side. She had a selection of vets surgery details on her phone just to make sure she knew where to get help for the dog if needed. She and her wonderful dog had the time of their lives. They thinking of doing the C2C this year. Last year they walked Offas Dyke.
I have a cat and she refuses to walk to the top of the garden, so I'll continue with my solo jaunts.