Sorry about your broody, red. Boy, you sure are having a trial by fire. Chickens are capable of recovering from serious injury, so don't give up on her. I wonder if the dog heard the chick peeping and that set him off. We had a huge lab when I was a kid that never ever bothered the chickens, but a fuzzy chick was considered hor d'oeuvres. Chicks weren't safe from him until they were feathered.
Keep the broody warm and quiet and hydrated if possible. Putting a towel over whatever you are keeping her in helps. Maybe she will hatch the rest of the eggs for you.