I've just moved to Australia also, so I've been looking into these things as well :)
If you are working as a sole trader then you just need to add the income you earn from selling on eBay etc to your overall income when you do a tax return at the end of the financial year. Make sure you keep records of how much you buy stock for, how much you sell it for, the eBay fees you pay, your profit, and any other expenses.
Basically you need an ABN number if your income is $75,000 +. You need to register for GST once you are earning $75,000 and over and an ABN number is necessary to do this.
Once you have an ABN number you need to put it on your website (if you have one) letter heads, business cards etc - anywhere that is going to be circulated in public.
If you are working from home then don't forget you can claim tax deductions on business expenses (rent/mortgage, utilities, internet bill etc). So remember to keep receipts and all your bills for the year.
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I would strongly recommend that you find an accountant to do you yearly accounts for you to make sure everything is in order.
Usually it only costs about $300-$1000 per year for an accountant to do your accounts for you and file your tax return. It saves a lot of effort and it's well worth the money if you have a couple of different sources of income.