There's a couple of things to consider here. First, your first claim is considered a collision
claim but your next claim would be considered a comprehensive
claim. Comprehensive claims are viewed differently than collision as they are usually not the result of your error. Because you hit an animal, who obviously doesn't abide by the laws of the road, your insurance company doesn't view this at at-fault. Studies have shown that comprehensive claims will only increase your rate by a couple of percents.