Hi and welcome to BYC.
I have had a chicken injured by a dog before, too. What I would do is give her a soak in a mixture of warm water and diluted betadine, about the color of weak tea. That way it cleans and disinfects the wounds you found and ones that may be hiding under her feathers. After the bath, pat her down with a towel and then put her someplace good and warm. She needs to be kept warm and quiet. She is probably just a little bit in shock and sore from her injuries. Give her access to food and water. Some high protein treats will help her heal faster - mealworms or a scrambled egg. If you can keep her inside at least until the wounds scab over, that will keep flies off and other chickens from pecking at her.
Chickens are tougher than you think. She will probably be up and around in a couple of days.
Good luck!