He can have his litterbox, his carpet, his toys, and space to do a little binky in there even.
2003, Susan E. Davis and Margo DeMello, Stories Rabbits Tell: A Natural and Cultural History of a Misunderstood Creature, Lantern Books, ISBN 978-1-59056-044-0:page 81: As he got to know Susan (and her food), he sometimes raced around on the grass when he saw her arrive, or leapt into the air, kicking his hind feet above him, then shaking his head goofily after he landed. This is the “shimmy†that Southern noticed, or the “frisk†that Lockley described. Among domestic rabbits, it’s referred to as a “bunny dance†by some and a “binky†by others. It looks sort of like an epileptic fit—but it’s an unmistakable gesture of joy.page 94: ... a rabbit in a cage by himself doesn’t play much. He may flop on his side when he feels relaxed. He may run in circles when he’s excited—if the cage is large enough. He may even pop a binky if the cage is high enough.
2009, Trina Wiebe, Rabbits Don't Do Homework, Lobster Press, ISBN 978-1-897550-01-4:page 41: “It’s called a ‘binky’,†said Crystal. “It’s a rabbit happy-dance.â€page 65: Binky did one of his famous binkies. He darted down the length of the run, then hopped and twisted ...
(US, informal, childish) A baby's pacifier. SeePacifier. In the U.S. (Reg. 0334946) and a number of other countries, BINKY is a brand of pacifiers, owned by Playtex Products, Inc. Seehttp://www.uspto.gov
Verb
(intransitive, rabbit behavior) To perform a high hop, as when happy.
2003, Susan E. Davis, Margo DeMello, Stories rabbits tell (page 347)... there are photos of rabbits in gardens, on desks and in laps: with dogs, with hamsters and with Santa: and yawning, snoozing, flopping, binkying and eating.