Been there. I had one run out in front of me on a 70 mph interstate and I just got slow enough to bump her and knock her down. Slightly dinged up my front end but the deer got up and ran away annoyed at me. The brakes do work very well. The old Ford Taurus behind me had to dive into another lane with his brakes fully on to not rear end me.
You were lucky. My experience with deer was on a dark night on a trip to visit my mother. It landed on the windshield of my Thunderbird. Broke the windshield and left hoof prints in the hood. It then disappeared. The deer did not end up in my lap. Thank God for modern glass which kept it out of the cabin. You can imagine the hassle of getting it fixed when you are out of town.
My sister, living in Northern New Hampshire at the time, told me that if it had been a moose it more likely would have ended up on my lap. They are heavier and have taller legs.
I've had close encounters with a trickle of deer coming out of the woods.
I've had a buck jump a jersey barrier on my left to land on my hood and completely destroy the front end bodywork.
I've had a large buck leap over the front of my motorcycle @ 50mph leaving me with nothing but a view of brown fur in my field of vision. (No contact )
I've had a hawk bounce off my helmet while on the motorcycle @ 40mph.
I've had three fawn unassumingly mosey across my forward path on a two lane blacktop.
In all no personal injuries, but any one of them bordered on catastrophe. I'll continue to rely on a large dose of luck, keen awareness and evasive action, and whatever else that can help avoid the bad result.
"When I'm riding my motorcycle I'm glad to be alive . When I stop riding my motorcycle I'm glad to be alive ." -- Neal Peart