As a DM, a normal animal in my games will almost never fight to the death. It's just...that doesn't happen.
You burn a pack of wolves and they will run, unless they are starved to the point of madness. Also they scare easy. Make some phantasmal terrain to scare them off and move on.
But also, animals aren't stupid, and they do have consciousness, so any ability that lets you communicate with them can work, just like the Bard can talk down some bandits.
That said, if I were playing a druid in a campaign where none of that is true, I wouldn't shy away from killing animals, but I would insist on not wasting their body if at all possible, and I would probably try to scare them off and/or use nonlethal means to knock them out.
But I have never bought the idea of Druids as vegetarians. Every animist culture in history has believed animals to be fully conscious creatures possessed of a soul just like humans. No animist culture in history has been vegetarian. Being one with nature does not (need to) mean not eating animals.