A few years ago in traffic, a dog suddenly appeared in front of me by narrowly dodging the car just ahead of me in the adjacent lane. It was medium sized and might have been an Aussie mix of some kind.
My reflexes didn't even have time to kick in before hitting it going, I'd say between 25 and 30 mph. I was riding an old 750 Kawasaki 2-stroke, and pretty much just knocked the dog partially out of the way before bouncing over at least part of it. Actually, it happened so fast that I was never sure exactly what happened, but I managed to keep the bike upright (barely). I don't know what happened to the dog, but it was gone when I turned around and went back.
30+ years ago, A medium sized dog came out of a driveway and before I could even react I hit him. I was doing 30-35 mph. the dog came from the right side, my passenger was knocked off the back but held on to my waist and ended up dragging both feet on the left side of the bike. Luckily we stayed upright. We were scared but okay. The dog was dead, killed instantly by the impact.
My point is agreeing that momentum can keep you upright even after a hard impact with an animal
I agree with most of the responses. If impact is inevitable, brake and scrub off as much speed as possible before impact, and hit straight up and perpendicular to the animal path if possible.
Some years back on a club ride in the country, the K1000RT in front of me, with two good sized people on it, nailed a good sized kamikazee intent dog at about 35 mph. Bob kept the bike straight up and drove right over the center of the dog, no brakes at impact. Bob had no where to go, he was about mid-pack in our group, right ahead of me. Messed up the dog a lot, and the owner finished the poor animal off. Owner said the dog chased any/all vehicles all the time so he wasn't too ticked about it. The dog owner's insurance even covered it!
Good thing too, because the impact bent both fork legs back about 3"! Bob rode the bike home about 25 miles. He said it was like driving a shopping cart with a bad wheel.
No larger animals, like deer, is another matter. I coach my MSF students to first off , know and realize where dear are, what they like (cover and water source, though those are no garauntee), when you see a deer slow down as fast and hard as you can. Swerving is a questionable action as deer many times turn right back to the impact. Slow hard in a straight line and aim for the deers butt if possible. By the time you get there the deer may be gone.