This website http://www.weeds.org.au will be a more useful resource to home gardeners than the Weeds CRC website, apart from enviroweeds.
All you have to do is type in a plant name (common or latin) into the search box and it will produce a list of links on that plant. The first link will be a species description including country of origin, description and what parts of Australia it is problematic and where, if any where, it is a declared noxious weed. If the species or the genera to which it belongs is declared noxious in any state or territory then the second link is usually a comprehensive list of declared noxious weeds throughout Australia. If it is declared in any state or territory then the column corresponding to that state will contain an entry - either the weed's category or "unaccessed" (if it is yet to be categorised I believe).
You will also notice that at the very bottom of the page there is a "Noxious Weed" link that will take you to all the state based lists of noxious weeds.