I am not an Aussie, so I don't live in Boothby.
But I thought I'd chime in before the Aussie girls wake up because I have studied Australian politics.
'Divisions' are what we call electorates and I think you guys call districts, ie it is the area that elects a particular reprentative. Boothby is therefore an electoral district in South Australia for the Federal Parliament.
http://www.aph.gov.au/house/members/member.asp?id=TK6
I can't remember if we have any South Australians on the boards or not.