Do I need to pay tax on an online photography business?

If I register online my domain name and set it up, is it registered. Do I need to pay tax if I am in Australia and to register it as a business?

Yes,

try these sites

http://www.business.gov.au/Business+Entr...
http://www.ato.gov.au/
http://www.asic.gov.au/asic/asic.nsf

If you are a freelance photographer you keep records of your transactions and declare your earnings at year end (June 30), this is subject to your individual tax bracket.
If you register a trading name with the govt. you will be given an ABN (Australian Business Number) and have a little bit more legitimacy but still a sole trader is no different in that it effects your personal tax bracket.
The next level up is to incorporate where your business gets an ACN and an ABN and a flat 30% tax bracket and a ton of write offs but they're expensive to run, need tons of compliance and you'll be forced to open a super fund and pay your own super and most likely will have to file taxes every 3 months and pay provisional tax.

Registering a domain name is not the same thing as registering a business, be aware if you register a business name you will have to meet ATO deadlines for payments and such, it's more formal than simple freelance.

Good luck:)

If you make money, the gov always wants a share.