vacation1:
A non-predatory terrier is not a terrier.
Just like a scent hound that can’t sniff out it’s own chew toy is not a scent hound 
Domestic dog breeds were selectively bred and culled to have instinctive attributes. If an owner does not want a certain type of behavior, then obtain a dog that doesn’t have that behavior bred into it. You can train to have some control over certain behaviors, but a good well bred representative of the breed will never be rid of that behavior and you’ll not be attributing to the best mental health for that dog to try to train out an ingrained, instinctive behavior. So if you don’t want a bossy, howling shedding machine that pulls hard on a leash, don’t get a husky or malamute no matter how cute and fluffy they look. If you want a dog to be happy inside most of the time and only have walks or a dog park for exercise or mental stimulus then an Irish Setter is a bad choice but a pug is a good one. If you raise free range guinea pigs, a JRT is not the dog for you…and so on and so forth.
Just like with horses, you get the animal that fits your lifestyle and not your aesthetic ideal. (whatever you find cute)
OP, these things happen. Know what the top killer of tiny fawns would be? It’s other does. Seriously. Does very often will stalk and kill other does’ fawns by a hard strike to their heads. The most common death for them until they’re capable of outrunning other adults. Deer have an extremely strict hierarchy when together and even when not keeping themselves separate but crossing paths. At least twice a year I can hear them crashing through the woods and going after one another, the fawns shriek. It’s pretty awful, I find them crushed on my little 4.5 acres on a somewhat regular basis and have witnessed it a handful of times.
Many times when dogs come across a down fawn, they react surprised and confused because instinct tells that fawn to NOT move. So a living thing with very very little scent is confusing to them. Nudging, circling, licking, etc are all normal reactions. And a down fawn will eventually move when being touched and that can surprise and shock the heck out of even the most laid back dog, bolting away or a grab and shake are both normal surprise reactions. Your dog didn’t do anything abnormal and neither did the fawn. The mom will call and then forget. Nature’s way. They lose so many in infancy that Nature makes sure they don’t have a hard grieving process. 
