Peg and Cat are in their bedroom and they are excited because they have been asked to mail five important letters, one of which has a red envelope and is extra important. Peg sees this as a sign she is growing up and looks at her and Cat's height charts that have been drawn on their door. However, they want to share the letters equally but can't because five is an odd number, so Peg declares it a "big problem".
After a moment of Cat pretending to have a "jig problem" and a "wig problem", they decide to divide the normal letters between them and take turns passing the special one. When they get to the mailbox, a large dog is sitting in front of the postbox and he scares them, but Peg doesn't want to give up for fear that her mother will never assign her more tasks.
Cat believes that adult humans are fearless and wonders why. Peg suggests that it is because they are taller than children and most animals, so any threatening animals would be afraid of them. This gives her the idea to stand on stilts in a large trench coat with Cat on her head, wearing a wig, so they can pretend to be a single, tall adult and scare away the big dog. However, he is not scared, so they run away.
They come up with a bunch of ideas, none of which work (maybe because they're singing about it while they're doing it), and then the very important letter ends up on the dog's head. Peg reaches out and grabs the letter, nervously, and finds out that the dog is friendly. They can't reach the mailbox but they can by standing on Big Dog, who, it turns out that the mailman is scared of, disproving Cat's claim that human adults are fearless.
Afterwards, Peg's mother is proud of Peg and Cat and they sing a song about how they're growing and learning.
This episode provides examples of
- An Aesop: Don't judge based on size.
- Amazing Technicolor Wildlife: Played straight for Cat who's indigo but averted for Big Dog, who's brown and white.
- Ambiguously Absent Parent: We don't know why Peg's dad isn't around.
- Big Friendly Dog: Big Dog is a large dog who is very friendly.
- Disappeared Dad: Peg's mom is seen but her dad is not acknowledged.
- A Dog Named "Dog": A cat named Cat and a big dog named Big Dog.
- Good Parents: Peg's mom seems to be a good mother, and she and Peg seem to get along well.
- The Klutz: Cat's clumsiness comes to light when he trips and the wig lands on his head.
- Large Ham: Peg overacts in her usual way some of the time in this episode.
- Meaningful Name: Big Dog lives up to both parts of his name.
- Mister Strangenoun: Big Dog's name is two words.
- Nearly Normal Animal: Big Dog is mainly a normal dog, but sometimes barks with a tune when other characters are singing.
- No Name Given: We don't find out the names of Peg's mom or the mailman.
- Unnamed Parent: Peg's mother is present, but her name is unknown.
- With Catlike Tread: Peg and Cat sing about sneaking past Big Dog while trying to do so.
