There is not a federal law regarding this since auto insurance laws are up to each state to dictate. Usually a state allows the insurance company of the parents to decide when a child should be placed on an auto insurance policy. As a general state rule, all licensed drivers need to be included or excluded on an insurance policy. You should notify your insurance company of all licensed drivers in your household. It is left up to the insurance provider's discretion to decide if this should be when the child first gets a permit or if they will allow the parents to wait until the child has received a full driver's license.
According to the NJ DOBI (Department of Banking and Insurance) you should notify your insurer when your child is ready to obtain their driving permit. Any change in your insurance cost will either apply when the child receives a permit or license, depending on the insurance company’s rating plan.
The DOBI notes that failure to disclose all of the drivers in a household to your insurer can be construed as a form of insurance fraud, which is subject to policy cancellation, civil fine, or penalty under the New Jersey Insurance Fraud Prevention Act. Most insurers offer discounts for multiple cars, so it will most likely cost less for a young driver to be added to their parents’ policy than to purchase their own. However, any driver with a car titled and registered in their name can purchase insurance. Check with your agent, broker or insurance company to understand the factors to consider when making such a decision.
If you want to shop around for insurance for you and other drivers in your house, such as a teenager who is learning to drive you can start by getting a quote from an auto insurance specialist.