There was a cartoon that played either during Captain Kangaroo or another program featured girl with bushy brown hair She also had dog and bird similar to peacock?

You're likely thinking of the cartoon "The Adventures of the Little Prince" which aired on Captain Kangaroo!

Here's what matches your description:

* Girl with bushy brown hair: The Little Prince had a companion named "The Little Princess," who had long, brown, curly hair.

* Dog: The Little Prince had a loyal dog companion named "Pookie."

* Bird similar to a peacock: The Little Prince had a pet peacock named "Pierre" who often spoke and was known for his flamboyant feathers.

The show featured whimsical adventures of the Little Prince and his friends, often exploring themes of kindness, friendship, and imagination.

Let me know if you have any other details, and I'll see if I can help you identify the cartoon!