It really depends on what the repair cost will be. If the other driver gets a few repair estimates, you should have a better understanding of whether it's worth paying for the damage yourself or filing a claim.
Filing a claim where you were the cause of damage will most likely result in an increase in your rate. In Texas, the average increase in premium for an at-fault accident is $817 per year, based on our State of Insurance report.
If you want the dent repaired and the other driver doesn't have insurance then you can ask him to pay you out of pocket for the damage. If not, you'll need to file a claim with your insurance provider.
Animals cause all sorts of damage to vehicles, and not always because someone hits them with their car. Luckily, insurance companies don't discriminate over you hitting an animal or an animal hitting your car.