To answer your question: Yes.
I've been in the newspaper industry for more than 18 years and I can say with all certainty that the photographer could have captured the mood of that crime scene without showing that little girl. As his editor, I would not have authorized the publishing of that photo and would have furthered instructed the photographer to delete all copies of it.
As an industry standard, it is generally inexcusable to publish photos of bodies or white sheets. Photographers and reporters often arrive on scenes shortly after law enforcement, so they see and hear much of what the general public never sees and hears. That is no reason, however, to publish certain information.
In this case, it appears the photographer got caught up in the emotional side of his job, which he is trained not to do. Having said that, as a veteran reporter and editor, I have done the same --- but I have never crossed the line.
NOLA was terribly irresponsible on this one.