Gosh, I really don't want to be a wet blanket, but I must.
There are very few "dogs" that can still be considered wild...that you'd want to have as a pet. These domesticated dogs, while still appearing to be a tough breed, have one major failing...they love their owners, and their owners love them.
You can see this as you drive/walk around many cities: formerly "tough" dogs, with bandannas around their necks, heads out of car windows...tongue going like mad, or on a cold day...curled up at the pet owners feet, without a care in the world. The dog becomes more than a pet, it becomes a part of the family. You take it everywhere and, it loves the going. But a trip to Aunt Betty's, or a two hour romp in the park...isn't the Camino!
I doubt very much if, when you were hit with the desire to walk the Milky Way, you asked your dog if they wanted to go along. Oh, you may have been excited and said something like, "Butch, how'd you like to take a 800kn walk...huh, boy! Would you like that?" And, Butch, sensing you were happy (about something) jumped and twisted around and panted...with a big doggy smile...thinking, I know if I act excited I may get a big bone.
Consider this...if you haven't practiced walking long distances and broken in your boots, you're likely to have blisters and sore feet. But you can do somethings to arrest the problem. You can buy insoles, wear special socks, etc. if you do get a blister, you dab some ointment on...add a bandage or some moleskin and trek on. If you get tired, need to use the facility, etc...you say to yourself...SELF, I need to do this...and you do! But your dog, being domesticated...only wants to please you. So, when the dog is starting to injure its pads, when it picks up a thorn, or gets something caught between its toes...it presses on, because the dog loves you.
Now, I'll assume, you really love your pooch. You bring all the things you might need to make the family member happy. You share food, or carry special dog food. Even better, you get the dog to carry its own vittles. Boy, that's something new to your dog. You may even go so far as to buy "booties" to protect the dog. Ever see a dog fight another dog, sure they bite, but they also use their paws and the nails that are attached. There are wild dogs on the Camino...real wild dogs that, when hungry, or "in heat" will attack to get what they want. OOPS...I never asked the sex of your dog. THAT, could be a problem. But, whatever, because your dog has those cute booties on, their nails are covered and they're vulnerable.
When I hiked the Appalachian Trail, there were several hikers that had a dog along. The lean-to's aren't that big, so when the dog was brought , the owner would ask if it was OK if the dog came inside...almost to a person we'd say NO! Not to be harsh, but because the dog wanted company and would walk all over our gear, track mud on sleeping bags, salivate into cooking pots and, bring in fleas and ticks.
When dogs get excited, they often urinate or defecate...right there! There can be someone else's, pack, bed roll or lap. That's not fun, and one of the reasons few albergue's allow dogs.
I love dogs, I've had many and will have one again. If you really want a superior Camino and truly love your dog, take some pictures and show them to your warm, healthy, probably fat dog (cuz folks will over feed them) when you get home.
Buen Camino
Arn