Choosing a Domain Name (DN)
The .com.au domain name is governed by a national regulation authority, Internet Names Australia (INA). INA sets rules and regulates matters relating to domain names. Registered companies and businesses must conform to INA rules and conditions before a domain name is approved.
The domain name you request via your Internet provider must be derived from your existing registered company or business name. You must supply your Australian Company Number (ACN) or your Australian Business Registration Number (ABRN). If you trade under your own name as a Sole Trader and do not have a registered business name, you can register a domain derived from your name.
Hypothetically for example, Acme Toys Pty Ltd could request the domain names - acmetoys.com.au, acme.com.au or at.com.au provided no other company has previously registered the names with INA.
The requested domain name must resemble the actual registered business name. For example, Acme Toys Pty Ltd would not be able to register - impact.com.au or goodtoy.com.au
The requested main domain name cannot be a common word. Acme Toys Pty Ltd would not be able to register toys.com.au
Hypothetically, a sole trader, trading under the name Lloyd Ernst could register the domain www.lloyd.com.au or www.lloydernst.com.au.
The following rules have been extracted  from regulations governing Australian .com.au domain names.
The amended Rule 5 permits common words to be accepted as third-level domain names under com.au, provided all the following conditions apply:
a) The proposed word is a distinct word within the the applicant's registered company name or registered business name - or represents the complete set of initials of all words within a registered Australian company name, excluding the initials corresponding to Ltd or Pty Ltd. INA reserves the right to reject offensive names, especially those coined ingeniously from the initials of company or business names.
b) The proposed domain name is not a generic product name such as software, pizza, cars, magazines, information, cash, credit, restaurants etc. The proposed domain name is not a generic industry or industry sector name such as banking, tourism, education, tennis, gardening agriculture, mining or consulting etc.
c) The propose domain name is not an Australian place name or standard abbreviation of an Australian place name (i.e Australia, WA or westernaustralia) or any name on the list of Australian Postcodes i.e. http://www.auspost.com.au/pcode96.htm.)
d) The proposed domain name is not a generic word describing organisations or industries such as company, corporation, industries, association, organisation, trust, fund, bank, cooperative, institution etc - nor a standard abbreviation of any of these words, such as Pty or Ltd.
Examples:
1. Ample Industries Pty Ltd is entitled to register the domain names, ample.com.au or ampleindustries.com.au or ample-industries.com.au or ai.com.au  The domain name, industries.com.au would not be acceptable.
2. Tennis Australia is entitled to register, tennis-australia.com.au but not entitled to register, tennis.com.au or australia.com.au
3. Minter Ellison is entitled to register, me.com.au or minter-ellison.com.au etc.

Domain name check-list
The following check-list will help ensure your domain name is not rejected by INA.
* You must supply the legal name of your organisation or company including your ACN or ABRN (Sole Traders excepted)
*  The domain name must be at least two characters long and contain only alpha-numeric characters ( i.e. a-z, A-Z, 0-9) and hyphens (-). The domain name must not start or finish with a hyphen.
*  The domain name must be directly derived from the the characters in commercial entity's full legal name. The characters must also be in the order in which they appear within the legal name. Characters that do not appear in the full legal name can not be used.
* The domain name must not be a generic word describing products, goods or services or industries, industry sectors, or organisations. Examples of unacceptable domain names include: beer (product), banking (industry), industrial (industry), company (organisation type). Generic phrases comprised of two or more generic words are allowed.
* The domain name must not be an Australian place name.
How long can a domain name be?
The maximum number of characters in a domain name is 26. This includes the periods (.) and the suffix. Remember, the http:// and the www normally found at the front of a Web address are not considered part of the domain name. The domain name WebCentral.com.au has a total length of 17 characters. We would suggest you keep your domain name as short as possible. This helps your customers to remember your email and web addresses.
Is your domain available?
Once you have decided on a preferred domain name, you need to check its availability. To check, simply access the WebCentral Check Domain web page at http://www.webcentral.com.au/checkdomain
Remember your domain name should be in the format businessname.com.au NOT www.businessname.com.au or http://www.businessname.com.au
When you select the Submit button, one of the following three possible responses appears.
1. This name is not visible to the DNS (Domain Name Server). This means the requested domain name is not being used. You may request this name for your domain name. See next section on how to apply for the domain name.
2) This name is not visible to the DNS. This name is pending in the AUNIC registry, awaiting the Domain Administrator's response to the request: This means the name is not in use but someone else has requested the domain name. Their details will appear on the screen. You should select another domain name.
3) This name is configured in the DNS: This means the requested domain is used by someone else and it can not be requested. The contact details of the domain owner is displayed on screen.