Glad to hear you are ok. Sorry to hear about your ride.
Being from Wisconsin we have lots of deer on the roadways. #1 lesson learned from my Father about deer when I got my license, NEVER under any circumstance swerve to miss a deer. Your car and your life are not worth it.
Insurance companies jack rates for driver induced accidents but minimally for deer hits. If the cause of an accident is because one swerved to miss a deer, insurance companies tend to view it as an at fault accident rather than a comprehensive claim. I.E. a big rate hike.
Even with hair in your bumper/fender, they will not view it as a deer hit as the damage is not consistent with a car-deer collision.
Best thing to do to avoid deer/animals is to brake heavily and aim for where the deer/animal was. If an impact is imminent release the brake and accelerate to raise the front end of the vehicle to prevent the animal from going through the windscreen.