According to the California state law, owners are generally responsible for any attack made by their animal, regardless of whether the attack happened in a public or private place. In private premises, the assumption is that the victim was there lawfully or with permission and knowledge of the owner.
In your case, it appears you would have to bear the liability for the attack–unless you can somehow prove that the child was in or entered your property unlawfully or, in other words, trespassed.
That defense, however, can be countered by the fact that the victim is a child. By law, a child can’t trespass because a child is considered incapable of having the intention to trespass. Simply put, a child is too young to conceive of doing anything unlawful.
Another defense is to argue that the child was unattended and show that someone else had fault (comparative fault). This is possible, but again, you would need to establish a couple of things, such as the circumstances that put the child on your property and why you lacked knowledge of it. Also, you would have to show how the lack of supervision by an adult led to the animal attack on the child.
You can explore these arguments, but honestly, the scales are tipped against you because you are the owner of the dog and the attack happened on your property. I advise you to talk to an animal bite attorney to get a clear view of the possible outcomes and what you can do about them.