Continuity mistake: Outside the windows of the house of Julia's friend it is daytime, but outside her front door it is night.
Continuity mistake: When we first see Eddie the radio announcer, his hair is blonde. But later on in the episode, his hair changes to a reddish colour.
Answer: The name of the pet is "Baby Puss." He has appeared in episodes, but only a very few. The first episode was probably "The X-Ray Story" from season 2.
Bishop73