The short story is the government is paranoid. They've made some really bad calls, like the cane toad, which has devastated huge areas of Northern Australia & is now moving south.
Although the Brits brought rabbits & foxes to the US also, you guys have native species which prey on them. We do not. Introduced species, both flora & fauna, have had a hugely negative impact on native species. The Aboriginal people exterminated the Tasmanian Devil & other species on Mainland Australia with the introduction of the dingo ~though that theory is now being questioned. However the ecological balance in most places is so delicate the utmost precaution needs to be taken. I know other countries think it's mad but we have lost thousands of species naturally [think bushfires] without risking contamination from outside sources.