I believe I do have a timeline of events that you might find elucidative.
Jerry asks his mum, Vanessa, if Midnight & Noone ever made any records. She tells him that they had not.
Jerry asks if she remembers any of the pair’s songs. She tells him about The Fellow with the Cello and Woof, Woof, Woof, attempting a short rendition of each.
She tells Jerry that the joke behind Woof, Woof, Woof is that it is a nightingale doing the dog impressions.