Not only Jared Diamond's Collapse but even Blll Bryson's Down Under make mention of how rabbits were deliberately indeed carefully added. Nobody really had any idea of the catastrophic effect of introducing species into an environment that had been geologically isolated for 65,000 years. Australia provided no natural predators for the large mammals that colonialists saw fit to offload.
These days, the Australian authorities are not taking any chances. There is the now-famous Australian baptism: pesticide spray that the cabin crew will bless you with as you arrive in Oz. There is also a whole range of things that you can't bring in to the country (above and beyond what you'd expect)and the penalties include anything from confiscation through AUS$220 on-the-spot fines, all the way up to 10 year in jail. You even have to make sure that your hiking boots aren't muddy. It's a different twist on the idea of putting out the welcoming mat. But of course I see the need.
But it took a little bit of googling and browsing to come across the list of prohibited imports. I wonder, if I hadn't been forewarned by colleagues who have been to Oz already, at what point would I have found out? When I was forced to bin expensive Chinese tea or souvenir erhu on arrival to Sydney?
[Added later: An inquiry to AQIS (Australian Quarantine and Inspection Service) pointed me at an online database where travellers can check specifically what conditions apply to specific good. Looks like I can bring in tea after all :-) ]