Anyone can register a domain. One does not have to be part of a business. There are many domain registrars on the web such as Go Daddy. You will need to have a credit card or paypal and you will need to put an owner's name on the domain name. Once you have domain, you will need to look into web hosting.
Registering a domain name on the Internet is easy with websites like GoDaddy.com. Watch how easy it is to register a domain name with the help of an experienced computer user in this free video on using the Internet....
Domain name registration is simple and you can usually do it fairly cheap. I would recommend you check out this website that will walk you through the process step by step
In Australia, currently there are 16 active second-level domains, all managed by auDA.
Open second-level domains (available for the public):
*.asn.au - for associations, political parties and clubs.