The short-legged baby marsupial from Tasmania's Flinders Island became famous when a video of him running along the beach surfaced online last month.
The eight-month-old was rescued from her mother's pouch after she was hit by a car in December, and Derek is now under the care of local resident Kate Mooney.
To give Mooney a temporary break from her voluntary duties, Tourism Tasmania is offering an Australian resident a chance to be "Chief Wombat Cuddler."
"The idea for the competition was spontaneous. When the video of Derek went viral on social media, it provided us with a perfect opportunity to keep people talking and thinking about Tasmania," John Fitzgerald, CEO of Tourism Tasmania, said.
Mooney, also known as the Wombat Lady, lives on Flinders Island, located at the north-eastern tip of Tasmania. She has been looking after the island's orphaned wombat joeys for the past two decades, single-handedly raising more than 100 of the animals, according to Tourism Tasmania.
She currently has 15 wombats, a protected species native to Australia, under her care in her 40-hectare home property. She usually releases them to the wild when they are mature enough.
The winner of the competition and a friend will be flown for a three-night stay on the island.
The competition is set to close on April 16 and the organizers have received more than 2,000 entries so far.