It is not easy to walk with a dog, but it can be done with some planning. Dogs are not allowed in almost all of the hostels and albergues. There are some villages where local dogs are unfriendly. It limits your sightseeing (fo example if you want to go to a Cathedral).
Anway if you sleep in a tent all the time, it is much easier with a dog, but you’ll have a different camino then others.
Caminoteca tip: important to bring a little backpack for the dog, so he could carry his own food and water.