Can I register this domain
Is there any law preventing this?
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You can register it in some registrars. It's not a problem, and it's completley legit to register something that is nonexisting.
But, In this case, when the DNS is propagated, you'll lose your domain name and everything.
I tried it already before 3 years for one client with a different name and he lost the money and domain.
As you are speaking about the .au ccTLD I will add that for
.com.au domain names as well as
.net.au domain names there is a regulated requirement by the auDA (registry for the .au ccTLD) which mandates that you have to have a verifiable business affiliation with the chosen name (such as if your company is named acme widgets and you choose a domain of acmewidgets.com.au). Furthermore for a .com.au or .net.au domain name business registration details such as an Australian Business Number is required as part of the verification process and most of the auDA certified registrar's are required to do at least a basic assessment of the domain name to make sure that it or a part of it does not appear to infringe on someone's trademark. Additionally as @Josip says the domain could be taken from you with no refund as the terms clearly state that the domain will be disabled for trademark infringement and that you as the customer will not be entitled to a refund.