I have no idea about the copywrite issues or legality of having a similar name.
But my question is do you want it, you will put a lot of effort into advertising it, and if people accidently leave off the .au, they are directed to what is another legitimate business, so you are advertising for someone else. plus if they get a bad name, you wear some of it as well. Just a thought
its best to go for an unique domain.. as Paul suggested its going to be hard with SEO etc… and they might bring legal team against you…. keep the .com.au domain and redirect to your new domain. so you will get people who wants the Australian site…
or setup a small site and create a link to your new brand..