If we are asking the question from an ethical standpoint, you have to decide on your own. Same goes for the decision to shoot a fawn. While I only have experience hunting in Northern states, I am not aware of anyplace that allows hunting before the time fawns are capable of survival alone. Nor am I aware of any state that does not allow a fawn to be taken on an antlerless tag. There are no strict biological or moral laws governing those decisions.
If we are asking from a management or conservation standpoint, there is no single right answer.either. It depends greatly on what you have to work with and what you want to accomplish. I hunt one property that has had a real overpopulation issue. On that property, any doe is a good doe, but I try to target the largest in a group, fawns or no fawns. However I have another property that is smaller, has a much thinner population and more hunting pressure. On that property I have found my hunting is better if I give mature does a little room. On that property I watch the doe herd carefully before skimming from the yearling does or even doe fawns using it. I think this helps to tweak the population without disrupting the herd dynamics.