The information you require is contained in the Land Protection (Pest and Stock Route Management Act) 2002 and the Land Protection (Pest and Stock Route Management) Regulations 2003. They may be accessed at
http://www.legislation.qld.gov.au/Acts_SLs/Acts_SL_L.htm
Schedule 1 of the regulations defines a number of species as not declared pest species including the Asian house gecko, the European hare, cane toads, sheep, cattle, donkeys and llamas black rats and sewer rats.
While these species may not be declared pests under the Land Protection Act, their keeping may be proscribed by local government ordinances. The methods of their keeping would also be covered by the Animal Care and Protection Act 2001.
