There are many Domain Registrars where you can buy a domain name.
There are some differences in deciding what that name should be, including thinking about using ‘keywords’ in your domain name, instead of your business or real name.
Will people be looking for you on Google .. OR what you do / the services you provide?

Also, understand that the Search Engines  like Google are US based and TLD’s are the best place to start.
TLD stands for ‘Top Level Domain” eg .com  .net. .org  .info

For most countries, the minimum purchase for a Domain name is 1 year..but in Australia it is 2 years.
In Australia .according to ” auDA’s regulations, or domains may only be registered to Australian sole traders, businesses or companies. This means that during the registration process, you will be asked to supply an Australian Business Number (ABN), Australian Company Number (ACN), State Business Number, Trademark Number or Incorporated Association Number to prove eligibility”
Read more on Australian domains registration here.
You will be prompted about the renewal of your Domain from your Registrar with a series of emails that go to the administrator email address on record with them, at 90 days, 60 days you will not lose the domain.
It can & does happen if no one is paying attention, so make sure the administrator email IS monitored regularly!
That can be a very costly mistake, as many 3rd parties see a chance to make extra money and snap up your Domain name- then you have to pay their asking price to get your Domain name back after you lose it!
We have seen that 3rd party asking price turn into thousands of dollars.

Also, it pays to search around, as there are differing prices in Domain costs from Registrars. There is no ‘standard’ fee.
Read some reviews on Features and Costs for some of the bigger Registrars before you wade in!

Remember for Australian domains , you will need an ACN or ABN.