It is unlikely that the dog will need boots if he stays on the trail (i.e.,if he doesn't put on 20 times the miles as you).  Dogs feet really vary as far as wear.  My older lab's feet are hard and tough, but on extended bird hunting trips his feet get destroyed (margins of the pads).  My younger lab's pads/feet are soft and supple and he hardly ever has a problem.  Neither usually have problems with backpacking, just bird hunting, which is much more abusive.  If the dog gets footsore, keep it on the trail to cut down on the miles.  Walk the dog on pavement to toughen feet up before, if the dog is not in good condition already.  After a week or two there won't be any problems once pads get toughened up. Trim nails to proper length at start (won't need it once you get going).
With my older lab, I've gotten to be a bit of an expert managing dog feet (during long bird hunting trips).  If the dog gets footsore, put boots on.  Some boots actually make the feet worse.   I've used cordura booties and homemade booties from duct tape.  Either way, I wrap the foot in vetwrap first.  Can't wrap too tight because you will cut off circulation and on some dogs wrapping or booties causes a toenail to dig in to the other toes - have to watch that.  HAving the dog in wet boots softens the pads, which causes they to be less tough and prone to damage.
In case of need due to injury, put a roll of vet wrap in your first aid kit.  Duct tape boots are the best with injured feet, IMO.  Wrap the foot with vet wrap up the leg.  Take a piece of tape that runs down back of leg, under pad and up front of leg.  Use strips crosswise to hold the first piece on.  Thinner strips conform to shape better.  They cab be pretty snug, but watch it.