Process time in the brain for a deer can be as short as = .001sec.
Time to travel to the muscles at 366 ft/sec = .01092 sec
Total time untill the deer reacts from the sound of the shot = .15968
Automated responses like that of jumping a string - do not travel to the brain and get processed - they travel through the automated pathways. In short they are controlled and originate from the spinal cord. These reactions occure much quicker than other responses. So the deer will react quicker than you state.
I still like my doppler effect
I guess you guys have never heard of the sonic disturbance momentum theory (SDMT)???