There is ALSO a task to deliver dog tallow (which you can get from merchants) to someone, so after Googling to see if the dog was a vital character, I figured, ok, it's triggered as a combatant now, I'll just kill it. But it doesn't WANT to fight, so I had to chase down this cowering dog and keep hitting it with my sword until (after a surprisingly long time) it died.
Then I said fuck this, I feel like a monster, and quit to return to my last save