When you as a US Citizen, receive more than USD 100,000 gift/ bequest/ inheritance from a non-US citizen individual or estate, you are required to report that on Form 3520 to be filed along with your tax return for the year of receipt. This form is required to satisfy your Reporting compliance of such receipts but the amount of inheritance is not taxable to you.
For the time period that this money is in a bank account in Australia before you repatriate it to the US or if you leave the money in the Australian bank account, you will have to also satisfy the foreign bank account reporting requirements under FATCA as well as the FBAR also known as Form FinCEN 114. Starting 2015, you can check a box on Form 3520 to state that they are satisfying the Form 8938 requirements to avoid duplicate reporting. Also any interest earned on this income from the Australian bank is reportable on your tax return Schedule B, if you pay any Australian taxes on such interest income, that can be claimed as a Foreign Tax Credit.

If your aunt does not have any US tax status (Citizenship/ Green Card or stay in the US), then there would not be any tax consequence. However, you would need to report the inheritance to IRS in Form 3520 by due date of your tax return in the the following year.