Detailed instructions on the export of pets to Australia are found on the website of the Animal and Plant Health Agency - GOV.GB.
Traveling to Britain with your pet is still possible after Brexit with an EU pet passport. For commercial pet exports, a health certificate from the TRACES system must be used, and the importer needs to make a pre-notification of the import in the IPAFFS system in the United Kingdom.
For more information on the effects on exports, please visit the Brexit pages.