It depends on where you live, some state has a no fault clause. It means it does not matter who is at fault, both insurance has to pick up the tab. If you live in a no fault state, your premium will go up.
I just got rear ended and thankfully AZ does not have no fault clause. The other's driver insurance company paid for the whole thing (my car was totalled). I also reported the accident to my insurance company (AMEX) but did not make a claim.
My insurance premium was just due about a month ago and the rate did not increase at all.
AMEX told me that it's a good thing that I reported it to AMEX insurance so the other's person company will not try to screw me.
Get the police report ASAP. you will need it! That deployed airbag at least costs $3,000, $1,000 to fix the windshield.
The cost to repair my trunk that was gone during the accident was close to $6,000 so you never know.
What if after more than 10 days, you did not report the accident and after knowing how much it will cost to fix your car, that girl's father refuse to pay you, then you are SOL.