I had that same exact experience in Idaho last year. I had a doe run out in front of me right around a corner. I hit the brakes harder than I thought possible after getting everything straight, I prepared for that sickening thud(anyone who has hit anything knows what I'm talking about) and just kept the fully loaded bike under control. When it didn't come I realized I had closed my eyes. I was going 60 as I spotted the deer and when I realized everything was okay I was going around 10 and had my first rear wheel liftoff experience. It helped my confidence in the bike and my abilities and it also humbled me about just how close you are to great injury. Needless to say I took it easy and took a break a few miles later.Plenty of things out there that are out of your control as well. Few weeks back I almost hit two female deer that ran across the road. I was leaned over at a moderate speed, nothing extraordinary.. I brought the bike upright and backed off the gas because I knew it was out of my control.
I think that's one really important lesson I've recently learned after years of riding. I'm now asking myself what animal/debris/driver-in-my-line might I encounter mid-apex, and do I have the room to react. At some point I accept that I am blind to those risks, but it comes with the territory of the sport.