Zachary first appears in That's My Baby, when he's being babysat by his aunt, Tina. Soon, Tina arrives at Daffy Duck's house to ask him to babysit Zachary, and Daffy agrees to. The two end up having a great time together, but when Tina's shift ends at Copy Place, Daffy becomes upset and does not want Zachary to leave him. Later on, at the park, Tina and Daffy are arguing when Zachary accidentally rolls down a hill in his stroller, and almost gets hit by Porky Pig's car, but he flies out of his stroller and into the air, where Daffy catches him. At the end of the episode, he goes home with his mother.
- Daffy mistook his name for Baby.
- Daffy also thought he was a female.
- Zachary hates clam juice.