A meteorite brochure put out by the Museum of Victoria in 2007 states that:
"In Western Australia and South Australia legislation means that meteorites are the property of the Government and must be lodged with an appropriate Museum. In other States, the finder is able to keep a meteorite."
I don't know if that's the present extent of State legislation - it's likely that in time other States will enact similar legislation, if they haven't done so already. Exporting a meteorite requires a Permit under Commonwealth law.
You might also find this interesting:
http://www.arts.gov.au/__data/assets...bservatory.pdf
Cheers -