Well, if you could get an Argentinian or a cowboy into the band I'd suggest The All Beef Paddies, but I guess Australia is better known for sheep.
Do you want a funny name or a serious name? Maybe The Fatal Shore, after the book of that name. Shillelagh Law? (See Finnegan's Wake) Or The Whacking Sheilas (as in "whacking shillelaghs", from Arthur McBride) Sheila and the Shillelaghs?
Sheel-na-Jig? (as in sheel-na-gig) (see Wonderbra thread, perhaps)Or Sheila Jig, I suppose. Summer In The Wintertime?
Mutton Accordian? Dingle Dingos? Wombats of Wexford?
Your theme song should be The World Turned Upside Down.