Here Comes Peter Cottontail (1971) on Netflix

When the Chief Easter Bunny retires, he chooses Peter Cottontail as his successor. However, the reclusive January Q. Irontail wants the position as well, seeking to revenge himself upon children everywhere for the destruction of his tail. He proposes he and Peter have a race to see who can deliver the most eggs. Due to his own carelessness and Irontail's meddling, Peter oversleeps and loses the job. Luckily, a strange man and a worm give him access to a time machine, so Peter can set things right. Unfortunately, Irontail is there with the intention of thwarting him every step of the way...