All household members should be disclosed regardless of age. In addition, their license status should be disclosed. If they are licensed, you may have the option to include or exclude them as drivers on your insurance policy. This applies to your children.
If your child is a minor, under age 18, and has a car of their own then they could get their own insurance policy however you as the parent would normally have to sign on that policy with your teen since it is a contract. If the child does not have a car and drives your vehicle than they should be added as a driver so that they will be properly covered by your auto insurance policy coverages.
Insurance company guidelines differ but in general insurance carriers will require you to list all licensed drivers in your household on your insurance policy. You should inform your insurance carrier when your child starts the licensing process, so at the permit stage, and your insurance company will tell you when he or she will need to be added.Your children may need to be added right away or they may allow you to wait until they get their junior driver's license or whatever the next step is in your state's licensing (GDL) process.
An insurer is permitted to consider all resident operators of an insured vehicle in rating of an auto insurance policy. This includes your child, even if he or she has only a learner's permit.
If you do not inform your insurance company about your child getting his or her license and they are not added at the correct time, according to your insurer's guidelines and the terms of your policy, than they may not be covered if in an accident. Or we have heard of situations in which the child would be covered for the accident but only after you have paid the premiums that should have been paid for the child to be on the policy and properly covered.
You can get a direct insurance quote here to see how much it would cost to insure your children.