The only way to get fast shipping into Australia is by air, of course that's usually also the most expensive, especially if you use a courier service. Unfortunately, shipping is always going to be a difficult issue to get around when it comes to international suppliers.
The US market is very different to the Australian one in may ways, for some reason local suppliers don't get behind dropshipping at all. What you will usually find is, that when you do get an Australian supplier willing to dropship, they will already be selling directly into the market themselves as well, but that's becoming common now for most, if not all dropship suppliers .... just the nature of that business.
When it comes to dropshipping, don't get tunnel vision in regards to a supply chain. What I mean by that is, just because a supplier doesn't offer dropshipping, doesn't automatically mean you can't dropship their products.
If you find a store that has a product that you think you can market, then the first thing to do is approach them as ask if they will; dropship for you. If they reject that, ask if they will blindship (sending the product to a customer, with the cost price blanked out on the invoice) It's essentially the same as dropshipping, but a process used in a B2B transaction most commonly.
Now I can't see many reasons why any business wouldn't agree to drop ship a product if asked. After all, a sale is a sale and so long as they make their margin, what do they care where they send it to. In fact you are acting as a salesperson for them in marketing their product, and a free salesperson at that. Now if for whatever reason they won't do either, what are your options?
You can always just go ahead and list the product anyway, then simply pay the store, pick it up and ship it to your customer yourself. The down side of that is that there is no stock control, so you may well sell something that is out of stock when you go to purchase it. But let's face it, that is an issue with a lot of dropship suppliers anyway, so maybe not a huge negative.
My point is there are many ways of doing this, just get a little creative and you can make all sorts of things happen, if you really want to.