USPS is way cheaper than FedEx and UPS. The cheapest you can go is USPS Parcel Post Ground, if without time constraint on your end, as it will arrive 4-6 weeks. You can also use Express Mail International , with free insurance and tracking - Link hidden: Login to view
Please note that if the package value (including postage) exceeds AUD$1000, the buyer will need to pay Customs fees prior to delivery. Customs will be assessing the item when it arrives in Australia.
You can also check out some parcel forwarding services like Link hidden: Login to view
They have accounts with USPS and FedEx and can offer deep discounts.
Hope this helps. :)