Welcome to SaleHoo, LetsEnjoyLife!
You don't need to be a US registered business to do business with US suppliers. If a supplier asks for a sales tax ID you can provide them the equivalent which is an ABN in Australia.
For US based dropshippers, shipping cost would be the least of their concerns as this will be shouldered by you or your customer.
You might also, try venturing into buying liquidated stocks or buy in bulk. Both will give you better profit margins compared to when you dropship products.
I recalled doing a search for you via a support ticket, were you unable to find any of the suppliers suggested suitable to your needs?
Talk to you soon!