Statute in Full:
Export Control Act 1982 (pdf - 542.57 kb)
Note the parts relevant to live export of of animals:
Part II - Export and entry for prescribed goods
This part of the Export Control Act 1982 (Cth) relates to exporters and licence conditions.
Part IIA - Accreditation of Veterinarians
This part of the Export Control Act 1982 (Cth) relates to the export of live animals in particular, as well as outlines the monitoring and approval system used by accredited veterinarians.