Originally Posted by PeterW
I decided on a 'best chance of surviving' strategy a few years ago
This is key, think about how things are likely to unfold and how you plan to act (vs. react). Deer, 'roos, etc. aren't gonna run you down from behind, nor are they likely to come strolling down the center of the lane. Consider the probable scenarios and come up with some preplanned strategies. No guarantee of success, but it sure does increase your chances.
Rule number one (for me): Where there is one deer, there is likely another following it, so look behind the one you see, not at it.
Rule number two: If you're really close to hitting a running animal, aim for it's ass, it will probably not be there by the time you reach it.
And like PeterW said, get off the brakes right before impact, you may be able to steer around it at the last instant, but not if you're braking hard.
YMMV, but this is my plan.