Delirium is a member of the Endless. That's her. She's a character from the Sandman series. In Brief Lives she gets a doggy from her brother. This is an excerpt from American Gods:
A young girl, no older than fourteen, her hair dyed green an orange and pink, stared at them as they went by. She sat beside a dog, a mongrel, with a piece of string for a collar and a leash. She looked hungrier than the dog did. The dog yapped at them, then wagged its tail.
Shadow gave the girl a dollar bill. She stared at it as if she was not sure what it was. "Buy dog food with it," Shadow suggested. She nodded, and smiled.
Who thinks that the girl in American Gods is Delirium?