Actually, he did have back up - the entire JL (minus Diana, who was conveniently off planet as I recall
) got taken down. Without Superman stopping him, Doomsday would, conceivably, have slaughtered everyone on the planet as there was no one else to stop him. There was no sign that Doomsday was going to stop at just Metropolis.
Diana fully believed the prophesy (hindsight is 20/20) and moved to save the JL from sacrificing themselves (which they would have) and leave the planet defenseless. She had no idea that she wouldn't die and fully expected to do so.