@Jennifer243, it depends on who ends up with the income - sounds like it might be your brother, and in that case you have nothing to worry about. There will be a paper (or electronic) trail that shows the income ultimately goes to him even though the AirBnB account is in your name. If you are banking any of the money yourself, though, you have to report it on your US income tax return.
And no, no one in my family is either Australian or owns property in Australia. I am sorry if that was confusing. I just wanted you to know that even though I am Canadian, I have some experience with US income taxes on foreign-earned income and have had to look things up before. Your absolute best bet is going to be reading the IRS website. Or maybe listening to @David126, since he is an actual American and seems wise. 🙂