No, children are held to the standard of care of a reasonable person their age. The rule provided by Restatement of Torts (2d) § 283A is: If the actor is a child, the standard of conduct to which he must conform to avoid being negligent is that of a reasonable person of like age, intelligence, and experience under the like circumstances.
Children can be held to an adult standard of care if they are engaging in an adult activity, such as operating a motor vehicle or flying an airplane.
In many states children under seven years old are not capable of negligence or cannot be sued for negligence. However, this is not uniform in all states. Consult your state’s judicial decisions and/or statutes to determine at what age a child and his parents can be sued for the negligent actions of a young child.