As some other posters have pointed out, this is a bit of a ballsy move by Tasmania. I commented on this development on my uni's Queer Collective page.
Under the Australian Constitution s 51 (xxi) and (xxii), the Cth has power to legislate on marriage and 'matrimonial causes' respectively. This is a concurrent power, so States can legislate on these matters provided it doesn't conflict with Commonwealth (read: Federal) legislation. The Commonwealth has enacted the Marriage Act 1951, so it's now a Cth matter.
In 2004, the Howard Government, in a move to deny recognition of same-sex marriages conducted in Canada, amended the Marriage Act 1951 to define marriage as 'the union of a man and a woman voluntarily entered into for life to the exclusion of all others'.
Tasmania now argues that this means the Cth has limited itself to heterosexual marriage, and Tas can now legislate for same-sex marriage, as if it's a separate category.
Personally, I don't think it would survive a High Court challenge, and it's really a measure taken to exert pressure on the Gillard Government. I'd be over the moon if it did succeed though