Green’s Dictionary of Slang

(Can./US) to run, escape.

1977		Ben-Veniste & Frampton Stonewall 166: Bennett confessed he had not wanted to get involved with Woods’s problem. He had told her to do her best and then jackrabbited out of her office.
1978		R. Caron Go-Boy! 28: Your best bet is to jackrabbit, and I mean tonight!