It will depend upon the guidelines of your insurance company if you are required to list everyone in your household as a driver. Normally a state's insurance regulator will permit auto insurance companies all resident operators of an insured vehicle in rating of an auto insurance policy. This may include your child, even if he or she has only a learner's permit.
Typically an insurance carrier will require you to list all of your household's licensed drivers on your policy since they will likely be driving the cars listed on the policy and thus the drivers need to have insurance coverage on them. Some insurance companies may allow you to exclude certain drivers in your household but if you excluded a person there would be no insurance coverage extended to that person if they did drive your car and were in an accident.
For information on Alabama insurance laws you can contact the AL Department of Insurance.
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