No...if you are conservative about your investments, I wouldn't bother, unless you want to retire to Australia, take vacations or open a business there, or have some other similar tie.
There might be some stocks you can't find in the US, or property or something else you could invest in within Australia, that would make this worth the trouble. I can't imagine doing it to get +3% interest. The extra interest is always balanced against risk that Australia will decide to print up more money than the US does, lowering the relative value of their currency. On the other hand, maybe you think it is worse in the US. But thats a gamble, not about earning 3% interest.
New Zealand used to be even better, like above 6% interest. Now rates are lower, everyone printing money like crazy I suppose....
If you do this, then besides exchange rate risk, you will need to file a TD F 90-22.1 with the US Treasury and check the 1040 box that says you have a foreign bank account and pay US taxes on that interest. Not filing the TD F 90-22.1 is potentially ruinous ($250,000 fine if willful, $10,000+ for negligence).
Australia has something like the US Patriot Act that requires that you prove ID at a bank to open an account. You get points for different types of ID. I remember I had to get my doctor to sign it in 2003 or so... copying a passport wasn't good enough.
ANZ and HSBC are reputable and have online banking. Be cautious investing just for rate. There are small lenders gone under down under (bad pun, I know). Don't buy anything representing a subordinated claim on debt (yeah the rate is higher but is 2nd class if there is a default and may recover nothing). And definitely don't just click on an ad. I think you'll want a real bricks-and-mortar bank if you choose to do this.
Good Luck - Paul