I have never heard of this game before so it comes as a cool surprise to find an interesting looking old game I know nothing about.

I must admit, and I'm not just making an obvious joke for once, I thought from the title it would be a Leisure Suit Larry style game with a frisky rabbit chap as the main character rather than a platformer. Jackrabbit sounds to me like a combination of the phrases "at it like rabbits" and "banging like a jack hammer" and of course jazz is an euphemism for porn - guess I just got a dirty mind though!