It will depend upon your parent's insurance company's rating system but typically adding a teenager or newly licensed driver to an auto insurance policy is costly and can raise rates by $1000 or more and even double the rates. However the young driver needs to be added to the policy so that they are properly covered when they drive.
According to the Canadian insurance company Kanetix if your child has their first level of driver's licence (G1 in Ontario), they are required to have a licensed driver in the car with them at all times. Since they are under constant supervision when behind the wheel, insurance companies consider their risk of accident to be relatively small, and generally insurers do not require people with this level of driver's licence to be added to an insurance policy.
As soon as your teen is licensed to drive on their own (G2 in Ontario), you are required to report this material change in risk to your insurance company and arrange for coverage for your teen.
Having completed an approved driver-training course should be in your advantage though regarding insurance rates. New drivers can receive significant discounts off their insurance for the first 3 years they are licensed if they have driver training.
The cost of adding a teen with a G2 to an insurance policy will vary depending primarily on the type of vehicle(s) you own, the age of the new driver and the young driver's history. A premium charge will be applied to your parent's insurance. All G2 drivers residing in the parent's household and driving an automobile must be added to their insurance policy.
Credit will be given for one year's driving experience for G1 and the driver will receive a rate reduction of 10 percent, if accident and ticket free, for all coverages where the driver's experience is used as a rating factor for a period of one year. Driver training discounts will also apply where applicable.
So in general adding you to the policy can up the rates by $1000 - $2000, so doubling the cost of your parents insurance is possible depending upon your parent's insurance company's rating system. You dad should speak with his insurance agent to get a quote for how much it will cost to add you to the policy now that you hold your G2. Be sure that he mentions your driver's education course to get a discount for that.