I had this same exact thing happen in my neighborhood driving the kids home from school. I wasn’t going more than 20-25mph but the dog ran out from behind bushes and just went directly under my hood. There was no time to react. Pup didn’t make it. 
It was the most terrible day- I know how you are feeling. Sounds like your outcome with be better 
Accidents happen and this was def not your fault. The owner will be feeling just as bad wondering if they could have prevented it
Hugs! 