I think you are right to ask policeman for a report.

There is a 13months old baby in the car, anything could happen in the future. And they will sue if you have money. It is much cheaper to pay the fine for not carrying insurance paper than get into a difficult to prove lawsuit.

You should call insurance company. Very likely, the other party will call; then insurance company will talk to you anyway. Call and get your side's story in is very important.