Welcome to Fluther, by the way.
You certainly will not go to jail unless there is some particularly aggravating circumstance involved here. The California jails are already full enough with real criminals that they aren’t putting people in stir for cracking the lens on a brake light and failing to report properly.
Since you arranged to have the claim made on your insurance, then obviously you have identified yourself to the driver of the other vehicle. Therefore my assumption is that you have apparently failed to notify the police, and all the prosecutor has to go on is the anonymous (most likely) call to the police notifying them of the damage, and your plate number.
Get together your paper for this:
Whatever notification you gave to the other driver
A copy of the other vehicle owner’s claim, which should include the date and place of the “offense”
A statement from your insurance company that the claim was paid
See if you can make an appointment with the prosecutor prior to the court date and review all of this. This is going to show the prosecutor that you did everything you needed to do… except notify the police. There may be a small fine for that, and the prosecutor may want to take the case to court to press that, if he wants to be a dick about it. But more than likely he will drop the prosecution, give you a stern lecture about notifying the police—and putting the fear of God into you (which has apparently already happened anyway)—and the thing will end there.
There’s no point in him taking a “case” to court when the only issues remaining are purely procedural ones; court time is too valuable for that. Your interview with him, if you can arrange it, should help to convince him that there is nothing at all to prosecute. If you’re organized and think this through, you should be able to handle the whole thing without an attorney, though it will cost you some time.
Hopefully, you won’t have to enter a plea at all.