You can register/purchase your domain name from numerous online companies called a “Registrar”.
Accredited registrars can be found here http://www.auda.org.au/registrars/accredited-registrars/
Separate companies to register your domain and hosting?
- using the same company is simpler, one bill and same notifications system
- Seperate companies makes it much easier to change hosting companies in the future.
- whois check: whois.domaintools.com | ozwhois.com.au | whois.auda.org.au
- Use correct emails: expiry notifications
- privacy services
- fake or real details?
- ignore all the upsells
- choose hosting on its own merits
- check the fine print of free domains. Do you own it? Can you move it?