Yes. If you earn $400 or more you need to declare it as part of your income on your US taxes, whether or not you get a 1099 and regardless of the communication used.
Realize that in today's world "Work done via the internet" means nothing to the IRS. It is still earned income. The only reason "via the internet" may matter is on a Schedule-C and your deductions because you'd clearly not be claiming travel expenses, but you may be claiming ISP expenses.
You don't need to file anything in AU if you live in the US (you pay taxes where you live, not where the client lives). But you definitely are expected to report any income over $400 in the US.
If you are a freelancer, the minimum you need to file a tax return is none of the above. The amount of money you need to earn and to file a tax return is $400. Yes. That is not a misprint. It is $400.
To be clear, this is not true of the group of people who call themselves freelancers and who are paid on W-2’s. It is true for the freelancers who get paid for the whole amount they earn, do not have any taxes withheld, and have or should have their income declared on a 1099.
Why is the number $400? While you may not owe any income taxes, as a freelancer, you must pay self-employment taxes in addition to regular income taxes. Self-employment taxes start if you earn $400 or more. Therefore you must file a tax return if you gross $400 or more.
If you have business expenses that should be taken into account, do not expect the IRS to know that. You must file a Schedule C or Schedule C-EZ that indicate your expenses. That way it may be that you don’t owe any self-employment taxes.
For example, you earned $5600 as a freelancer but you had $5300 of expenses. Your net is $300. As a result, you wouldn’t owe any taxes, either income taxes or self-employment taxes. You must, however, file your returns because you grossed $400 or more. If you don’t, you could well get a letter from the IRS with a bill and a request for an explanation for why you shouldn’t owe this money. I believe it’s better to file the return and avoid the correspondence.
If you earned $5600 and had $4600 of expenses, your net is $1000. You wouldn’t owe any income taxes but you would owe self-employment taxes and would have to file a tax return.