Sentence:  [http://books.google.com/books?id=ZCS5yfJ7NAEC&pg=PA94&dq=binky 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 “<WSD>binky</WSD>” by others. It looks sort of like an epileptic fit—but it's an unmistakable gesture of joy. / [http://books.google.com/books?id=ZCS5yfJ7NAEC&pg=PA94&dq=binky 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 <WSD>binky</WSD> if the cage is high enough. 
Meaning of the word marked with <WSD> tags:  A high hop that a rabbit may perform when happy.