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.

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.