Accident Report Question

Hello. I was recently in my first accident today,I rear ended someone in Terrebonne Parish Louisiana. There was barely any damage and no one was hurt but police where called and an accident report was made. I received a ticket for careless operation. The lady I hit is willing to let me pay out of pocket for the damages which are very minimal it's just small scratches and a small dent and she is willing to keep insurance out of it. I am going to call the DA's office to see if I can either pay extra or do a defensive driving course to keep it off my record. If I am able to keep it off my record,do I still need to let my insurance know? Will my insurance still see the accident report if I am able to keep the ticket off my record,and if so should I still let my insurance know,even though neither of us are going to file a claim? Any advice is appreciated. Thank you