Answer: Banana
Juno was drinking from a huge Sunny Delight container, thinking about the chair that started it all. I noticed in the scene of her reflection that Paulie was NOT sitting on THAT brown chair when Juno sat on his lap. Maybe it was a continuity mistake or maybe the filmmakers thought no one would ever notice. The chair Paulie was sitting on had a striped pattern, also seen again in his Tic-Tac fetish moment, and was more roomy than that single reclining brown chair in the opening sequence.
I never did figure out whose dog Banana was, but it wasn't a MacGuff pet. Her step-mom was waiting to get dogs after she moved out, as Juno was allergic to dog saliva.