Check with your state for the legal requirements if you hit a domestic animal like cats, dogs, cows, horses, etc. There might be severe consequences if you don't follow the law. My suggestion is you must stop and call the 911 to report the accident to the police. If you leave you could possibly be charged with leaving the scene. In most states, a pet is considered personal property and a hit and run that results in property damage carries a criminal penalty.
Only get out to go to the animal if it’s clear there is no danger of you being hit by oncoming traffic. Don't move the animal unless you are sure it is safe to do so. Wait with it until help arrives. Only move the animal if it looks like it is going to get hit again. Be careful a hurt and scared animal may lash out and bite when approached. Be very cautious for your own safety. If you have to move the animal use a blanket.
Professional Pet Sitting Services offered in the Upper to Mid-Pinellas County Area