Hi danchan, and welcome to the site.
Firstly the choice of having an ABN is that of your own, you don't need it to sell online, however it is required if you are going to trade as a registered business.
That being said, an ABN will also be required by most genuine wholesalers if you wanted to buy wholesale, but is not a requirement of drop shippers.
An ABN is quite simple to get, just contact the Australian Taxation Office to have an application processed.
Choosing to register your business is again a personal choice, and you have a few options, a company structure being one, but not a cheap option.
If you are doing this on your own, and you do want to trade as a business, then I would be suggesting registering as a Sole Trader. You can do this by contacting the licensing department in your state.
I think that would be Consumer Affairs in Victoria, or they may well have a specific licensing department set up like Qld Smart Licence, which is still part of the Consumer Affairs department here.
Regarding Drop Shippers, I'm going to assume that we are talking about ebay here as where you want to sell, so you are not limited to Australian drop shippers alone.
You can offer products from drop shippers all over the planet, so long as they will ship to your customers. Now, the issue that does come into play is that you have to accurately list your items location.
That means the location of the item you are selling, not where you live, unless you are having the items all delivered to your home first and then shipping from there.
I would suggest contacting support@salehoo.com with some specifics on products that you want to drop ship, and then they will be able to provide you with some names to check out.