Can you please tell me of some laws that conflict between federal and state level?

Federal and state laws should not conflict. Under section 109 of the Australian Constitution, if a state parliament and the federal Parliament pass conflicting laws on the same subject, then the federal law overrides the state law. While conflicts can happen, they are usually resolved through the legal system. 

The High Court of Australia the power to resolve disagreements between the federal and state governments over their law-making powers. It is up to the High Court to decide whether the Constitution gives the relevant parliament the power to make this law. A law judged by the High Court to be unconstitutional is then overruled. 

Some of the areas where the federal and state or territory parliaments have made conflicting laws in the past include the environment, health, education, heritage protection, euthanasia and same-sex marriage.

For example, the Parliament of Victoria had made a law that restricted access to a fertility treatment to women who were married or living with a partner in a long-term relationship. In 2000, this law was contested for conflicting with the federal Sex Discrimination Act 1984, which makes it illegal to treat someone differently based on whether they are married or not. The court found that the state law was inconsistent with the federal law. As a result, the restriction was overturned, allowing single women to access the fertility treatment.

Three levels of government: Federal, state and local.

Three levels of government in Australia

Parliamentary Education Office (peo.gov.au)

Three levels of government in Australia

Three levels of government: Federal, state and local.

Parliamentary Education Office (peo.gov.au)

Description

The three levels of government  – the law-making bodies in Australia. The Federal Parliament is located in Canberra, the nation's capital. State/territory parliaments are located in the capital cities of each of the 6 states and 2 territories. Local councils are located around Australia in each local council division.