You are generally running a business if the activity is carried out in an organised and coherent way. Also, if you are intending to make a profit; although note that 'intending to make a profit' doesn't mean you must make one. The intention must be there.
What is a hobby?
An activity primarily conducted for private pleasure or recreation.
Areas to consider:
The scale of operations.
The volume of transactions.
The commitment of time, money & effort.
The pattern of activity.
The financial results.
The type of activity.
What is your intention behind performing the activity.
In most cases your business will 'officially' start when:
You buy or sell stock.
You start performing your services for your customers.
When your activities are at a significant, profit-motivated level.
OKAY, MY HOBBY IS MORE LIKE A BUSINESS - WHAT NOW?!
Consider meeting with an accountant.
Consider a business structure.
Most common types are; sole trader, partnership, Company
Get in the habit of keeping receipts in an orderly manner for all business transactions. Ensure you have a separate business bank account.
Do I need to register for GST?
Consult with your accountant. If your taxable activity turnover will exceed $60,000 per annum you must register. You can voluntarily register and this would be upon advice of your accountant.
The most vital step to starting your business is to receive initial expert advice.
Feel free to contact me for a no cost, no obligation, initial interview