Sorry to hear about the hit and run, mine got keyed last month and I'm stripping it down to fiberglass for new paint.
Placing a claim with your carrier will involve your deductible if you have one and could increase your rates since claims history will be generated, granted your premium could go up anyway on an annual basis depending upon how many claims are paid by the carrier for the year at which time they pass their expense on to all policy holders including those who haven't placed a claim.
So you could do the good thing and pay it out of pocket and still get hit with a higher premium due to others who filed claims or you can place a claim and have them pay for it and have your rates go up and know that at least you helped contribute to the increase

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You would be better off with a police report, it's a preferred standard with insurance carriers and some require them. I drove mine to the police department the next day and met an officer, showed him the damage and he gave me a case number that you'll pass on to your carrier when you file your claim. Take pictures for your records and maintain a log of everything you do related to your claim from the date and time and officer you report the damage to and then every phone call you make to your agent or insurance company, body shop, etc. You shouldn't need this but it's better to have it documented just in case, CYA.
Eric