Hi Leanne,
In regards to being cost competitive on shipping, that will come down to what your Drop Shipper is charging really. That said, with the Aussie dollar trading out of it's skin and sitting somewhere around $1.07 US currently, I would suggest that there has rarely been a better time to be using US suppliers for Australian sellers.
Now if you are Drop Shipping to an Australian market, then the strong Aussie dollar should make shipping on your items from the US look like a pretty good deal to your customers, but again, that will all come down to what the supplier is charging for that shipping.
Cheers