Thanks for your question.
Australia has three levels of law-making – federal, state and local – that work together to provide Australians with the services they need.
Some of the responsibilities of federal, state/territory and local governments overlap, but generally each level of government provides different services to Australians.
Education is one of the responsibilities that overlap federal and state governments, although different aspects of education are generaly divided between either state of local. For example, the federal minister for education would be responsible for areas such as childcare funding, university funding, international education and research. State education ministers would be responsible for teacher training, school resourcing and curriculum.
The Department of Education and Training is responsible for national policies and programs that help Australians access quality and affordable early child care and childhood education, school education, higher education, vocational education and training, international education and research
For more information you could visit the federal Department of Education's website and the websites of state departments of education and compare their different areas of responsibility.