The ATO says you should only register for GST if:

• your business or enterprise has a GST turnover (gross income minus GST) of $75 000 or more
• your non-profit organisation has a GST turnover of $150 000 per year or more 
• you provide taxi or limousine travel for passengers (note: the ATO says that pets do not count as 'passengers') in exchange for a fare as part of your business, regardless of your GST turnover – this applies to both owner drivers and if you lease or rent a taxi
• you want to claim fuel tax credits for your business or enterprise.

See ATO Reference