Learn English – What does the word ‘dicta’ (‘dita’?) mean in the song ‘Who’s That Chick?’

Hunt the Hare is the title of a traditional Irish jig. That's probably why it is capitalized. Reference: https://thesession.org/tunes/4426

You're right about rig, it's an archaic word for a trick or prank. From Brewer's Dictionary of Phrase and Fable:

Run a Rig (To).

To play a trick, to suffer a sportive trick. Thus, John Gilpin, when he set out, “little thought of running such a rig” as he suffered. Florio gives as a meaning of rig, “the tricks of a wanton;” hence frolicsome and deceptive tricks. The rig of a ship means the way it is rigged, hence its appearance; and, as pirates deceive by changing the rig of their vessel, so rig came to mean a trick to deceive, a trick, a frolicsome deception.

I think that jiggelin' is a contraction of "jiggling buttocks" - "jiggling" being similar in meaning to "wobbling".

http://www.thefreedictionary.com/jiggling

 To move or rock lightly up and down or to and fro in an unsteady, jerky manner

So, the speaker is saying that she simply wants to lower her jiggling backside (or perhaps her jiggling body as a whole) towards the floor (eg the dance floor of a nightclub), presumably as a dance move - ie, that she simply wants to go dancing.

She is finding the conversation with the policeman frustrating, as it is preventing her from reaching the aforementioned night club, where she can proceed with the "jiggelin'".