Continuity mistake: When Fred and family start their drive toward Jellyrock Park, the trailer has one window and a door on its right side (behind Wilma's side of the car), but when they reach Jellyrock that side of the trailer now has two windows and the door is gone. (00:11:50)
Continuity mistake: When Fred walks into the room with a snack for a second time, he goes back and returns with a purple salt shaker. In the next shot, the shaker is blue.
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