Symbolism, Imagery, Allegory
We imagine that Mr. Babbitt looks something like this.
Okay, now that we've put that image in your head, let's talk about who he is and why he's important to the story. First, the most important question—what on earth is a high school student doing walking around talking to a stuffed bunny? We really have no idea—it might be one way that Darla copes with the bizarre feelings that cause her to do things like almost blind her brother with Drano. But regardless, Mr. Babbitt is an indisputable presence in this book.
The real significance of the bunny becomes clear in the Madmen's first meeting with their new therapist, Dr. Schwinn. "Your file mentioned Mr. Babbitt," Dr. Schwinn attempts to say when Darla whips him out. She is cut off by this winning remark: "Did it mention that Mr. Babbitt is usually the smartest person in the room?" (25.53-54). Ha.
Darla uses her usual sarcasm here in an attempt to keep Dr. Schwinn off balance, but really, there's some truth to what she says. There are very few trustworthy, stable people in these kids' lives—the majority of them have parents or relatives who are mentally, physically, and/or sexually abusive. All of the Madmen are crying for help (as loud as they can without ratting on their parents), and perhaps Darla's routine of communicating with a stuffed animal is the loudest.
At the end of the book, when Gratz takes Karl to set up his bank account and they talk about how Karl could potentially help the Madmen anonymously, there seems to be hope that things will change. But, for the bulk of the story, Mr. Babbitt is a sign of just how messed up things are for Darla and her friends. We might spend a lot of the book laughing at the absurdity of Darla's conversations with him, but ultimately, he's someone she really needs. After all, you're never too old for stuffed animals.