Yes, your business will require an Australian Business Number (ABN) if you a reselling online in Australia. An ABN identifies your business to potential buyers and is also a requirement for registering a .com.au or .net.au domain name for your website. If you wish to claim deductions for Goods and Services Tax (GST) you will also require an ABN. An ABN is set up by the Australian Tax Office (ATO) and you can even register one online.
In addition to an ABN, you will need to register an Australian Business Name (also known as your Trading Name) if your business name will be different from your full name.
You can register a business name at the same time as you are applying for an ABN or wait until your ABN has been set up and apply for your business name then.