First time Amazon user here, I've found some items that do not say "This item does not ship to Australia" but just before I make the purchase, I just wanted to clarify with you guys before I bite the bullet.
Added to this: are the shipping services used for Amazon -> Australia only used for those items which do not ship to Australia in the first place?
Check out https://www.myus.com/au/. If it is a one time or irregular shopping on Amazon, you can consider getting just a basic plan. Set up fee is us$10, no monthly fees and you pay only for shipping as and when you need them. You will get a unique myUS address so your purchases will get sent there. You then have 5 days to store your arrived package(s) to order your shipment from your MyUS service to Australia.
You get better value shipping rates and a longer storage time if you subscribe to their Premium membership where you pay a monthly fee - so a better value if you do regular shopping from USA online shops.