No, if all you have is liability coverages of property damage (PD) and bodily injury (BI) on your vehicle you would not be covered if you hit a deer.
PD and BI liability covers others that you may cause damage or harm to while in your vehicle, this coverage does not cover you or your own vehicle for accidents you are in.
To have your vehicle covered for hitting a deer you would need comprehensive coverage. This optional physical damage coverage covers damage to your vehicle if it is stolen; or damaged by flood, fire, or animals. Comprehensive coverage would pays to fix your vehicle's damages from hitting the deer less the deductible you choose.