Uh, this could be a lot worse than your premiums skyrocketing. Hope that their is very little damage and no injuries. Listen up: I have not brushed up on my Kentucky law in awhile, but in Florida it is a misdemeanor to allow someone else to drive if you know they don't have a license. If someone got hurt and they realize the driver does not have insurance, but you do, they will sue you (your insurance company). If you knew they did not have a license that looks bad. Your insurance company may not want to pay up if you knew that your freind did not have a license, which would leave you on the hook, if the victim sues. The other problem is that your insurance company may not want to cover you if DON'T report the accident. Normally an insurance company has lawyers that defend the insured (you), but if their policy (contract) says they don't cover for situations where you knew somone did not have a license then you would have to hire your own attorney if your insurance company and their attorneys bail on you. You could find out who your friend hit and see what the damage is. If they are not injured and their car has just a little damage, you could offer them a little money and say your friend feels bad. But if they pick up at all that you could be at fault--a little or a lot--a lightbulb could go off in their head and they come after you and your insurance company. So that is your judgment call there are pros and cons in offering to settle in any case or situation.
The good news is that there were no other people involved. Hopefully your friend was not injured. If he/she was they may make a claim for their injuries. if you have not reported the accident this may become a problem.
Your drunk, unlicensed friend had a one car accident, of course he's reponsible for the damages. If your friend was not hurt and all you have is property damage and your friend is able and willing to pay for the damage then there's no need to turn t in to your insurance company. But I suspect that your friend has no money, and is denying responsibility, leaving you with a wrecked car. So you can: 1) turn it in, get your car fixed and let your insurance go after the friend for reimbursement (you can join in to try and get your deductible) Your rates may go up but you get your car faster; or 2) fix it at your own expense, and sue your friend for reimbursement, no increase in insurance but you may never get your money from your (now former) friend.
I'd turn it in, let the insurance do what I've paid them for all these years and pursue the friend for the deductible. Good luck