Get insurance involved for $1800 in damage?

The short answer is no but there's a lot to unpack here.

1. First, most insurance companies require you to report any incident, even if a claim is not filed.
2. If he were to file a claim, it would definitely impact his rates for the next 3 to 5 years. In the chart below, you can see how an at-fault accident would impact your rates in NJ.
3. Your friend should consider if the value of the damage exceeds the rate increase he would receive. On average, an at-fault accident raised rates a total of $4,230 in NJ in 2017. This plus your friend's deductible would exceed the total out-of-pocket expense he would save. Because of this, I recommend paying for the damages out of pocket. Bear in mind, because of this age, this is probably much lower than what he would expect. Young male drivers tend to pay above the average premium considering the risk they present.

The last aspect to consider is the other vehicle in the accident. Who is the at-fault driver? Without much context, there is not a lot of advice I can here. If you are the at-fault driver, the other vehicle would be covered by your liability coverage and in that case, I would contact your insurance company as they can be helpful in this process. Here is some additional information regarding the claims process. Best of luck.