I came in with a DUI on an ETA. Just be honest about it when you go thru customs, they'll have you fill out a form and then let you thru. I and another guy were doing same thing at the same time in immigration so I think Oz is used to seeing this. And it's rather an issue here too, so I certainly wouldn't worry about your ETA. The background check website said I could apply for it from Australia's Immigration and Border Protection, if my criminal offense was less the 12 months jail time. I didn't have to serve any time but the maximum jail time I could have gotten was 6 months. I just did a normal ETA and filled it out. They give you a form when entering the country that asks if you've been convicted of a crime so I checked it. When they see that you checked that on the form, they have another guy take you off to the side and ask you some questions. They asked me what it was, when it happened, and how much it cost for the ticket. He wrote it down and copied it and put in some file I'm guessing. So if I ever go back they'll probably ask the same question is my guess.