Ding couldn't be a more obvious symbol if he tried. When the first thing we hear about him is that "the sweet baby goat is exactly as nice as" (1.4.12) Piper, it's pretty clear that his job here is to symbolize all that's good and sweet and innocent in this world.
To this end, when Piper and Daisy get sent away from their home and separated from their family, they also lose track of Ding—a.k.a. their innocence—though they still hold out hope to be reunited with him.
Unfortunately, when they finally do find him, he's "covered in s*** and as thin as the thinnest thing that could still be alive" (1.26.25). Like their innocence after navigating the war, he's practically dead on his feet. And if that's not enough to convince you that Ding's state represents the end of innocence, a few moments later, Daisy "covered him with a grain sack and shot in in the head" (1.26.28). Convinced now? Yeah, we thought so.