Does your lab puppy get any human attention, are all of the female dogs spayed? Since labs are Gun dogs, they have a higher prey drive than some other breeds, I would never leave your 4 year old unattended with the dog. It sounds from your question like this aggressive behavior is a new thing, or has the puppy always had some amount of aggressiveness to her character?
I am thinking that your Lab is not getting enough exercise from you and you are not acting like this dog's master (alpha, pack leader).
Does your dog really get most of her attention from playing with another puppy? She needs your leadership and attention if you are going to keep her. She can not be allowed to be aggressive towards anything or anyone.
I hope this does not sound harsh, I am not meaning it too, but the cold hard truth is I think you should stick to smaller, non gun type dogs. You are not providing the exercise, human guidance and training this 11 month old puppy needs to have a happy life.
I think you should take this dog to the vet's and tell them what happened that way they can rule out any medical issues that might exist, but I do believe this dog is being aggressive because she thinks she is the pack leader and not you.
For the sake of your child's health, you should probably give this puppy to a rescue and let them find it a suitable home, where it can be inside, part of the family, get it's needed exercise and training.
I have a Golden Retriever/Lab mix, that is almost 4 years old, that has a high prey drive for small animals (rabbits and squirrels), while she loves the cats that live in our home, she does not like the cat that roams the neighborhood, that said my dog is well attended while outside, she is never left alone while out there, has been trained to be gentle and kind to family and friends, at the same time she is also a good watch dog. She alerts when strangers come to the door. She is sweet and loving, but she has been trained, gets lots of exercise (2-3 miles of walking a day) plus mental games and swimming and playing fetch. What I am trying to say by this description of my dog is your lab is not acting like a labrador should, it is going against breed standard.
I am very clear and consistent with her and she knows who is in charge and that is me and not her. Your dog's behavior is not common in the breed.
So please give this dog to a rescue, not to another uneducated person without much training knowledge base to work from. This puppy is going to require extensive retraining and behavior modification to ever be adoptable.
I hope this helps and good luck!
Owner of a Golden Retriever/Lab mix