Eliza Jane

Eliza Jane appeared in The Wubbulous World of Dr. Seuss episode "The Gink." 
Eliza wants a Gink and so The Cat in the Hat shows her all these other pets (including a bald eagle and a poodle that can draw), but she keeps saying "She wants something better." She adopts the Gink, only for the Gink to be very high-maintenance. He suddenly becomes very gloomy, and despite Eliza's best efforts to make him feel better, 
she decides to release him into the wild, wanting him to be happy.
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Eliza Jane
Eliza Jane