**Please Note - I do not know if this is the one that aired on Nickelodeon but it is from the '80's and it's full length so this one will have to have to.**
From Wikipedia, the free encyclopedia
The Velveteen Rabbit (or How Toys Become Real) is a children's book written by Margery Williams (also known as Margery Williams Bianco) and illustrated by William Nicholson. It chronicles the story of a stuffed rabbit and his desire to become real through the love of his owner. The book was first published in 1922 and has been republished many times since.
The Velveteen Rabbit