Getting insurance while having a learner's permit depends on state law and the policy of the insurance company you have contacted. Typically you will need someone with a driver's license on the insurance policy with you. After that you can most likely be added as an unrated driver.
According to the motor vehicle commission of New Jersey proof of insurance is needed at the time of registration. I would contact an insurance agent to get quotes for the type of insurance you need. Or better yet go online with us and get a quote for your New Jersey insurance needs.
Our company in New Jersey does require a license and registration in order to purchase your policy.