For FOI requests made under Commonwealth law (i.e. to a federal government agency), there is no cost of making the request. However, you will probably be charged for access to the information. This access charge will depend on how long it takes to compile the information and make a decision about whether to grant access. You will be given an estimate before being required to pay. You can request that the fees be waived or reduced (in particular if there is a public interest reason or the charge would cause you financial hardship) but the agency does not have to waive the fee. More information is available from the Office of the Australian Information Commissioner.
For requests made under NSW law (i.e. to a state government agency), there is a $30 application fee and you will also be charged processing fees. The processing fee may depend on how long it takes to compilethe information and make a decision about whether to grant access. You will be given an estimate before being required to pay. You can apply to have the application fee and/or processing fees waived or reduced. More information is available from the Information and Privacy Commission of New South Wales.
The situation is different in each state and territory.