They do have a team (the Tasmanian Devils) in the VFL (Victorian league), and a team in the national league is a popular topic among supporters as well as the state government (one of the potential sponsors of such a team).
Unfortunately Tasmania's small population and low sponsorship potential have resulting in the state not being represented in national basketball, soccer and netball leagues.
Crown Princess Mary of Denmark was born and raised in Taroona, a southern suburb of Hobart.