A deer hitting your vehicle may be considered an "act of nature" or "act of God" so that the accident is not considered to be an at-fault one or be counted against your driving record, but this will depend upon your state's laws. You can check with your Department of Motor Vehicles to see how this type of accident is categorized in your state.
Damage caused to your vehicle by a deer would be claimed under your comprehensive coverage. Whether this sort of claim would cause your insurance to go up will depend upon state laws and your insurance company's rating system and guidelines.
When placing your claim with your agent you should discuss if this type of claim will cause your rate to increase. If your rates do rise you may want to shop around for more affordable car insurance. You can start here by getting an auto insurance quote online.