From the 27/8, Newegg now offers free shipping to Australia using the World EggSaver Standard option across most of their products.
There doesn't seem to be any official announcement but I've checked quite a few items to confirm that its now active.
UPDATE: Official announcement here: https://www.newegg.com/promotions/marketplace/2018/18-2562/l...
Please note that there are exclusions, such as bulky computer cases.
Some listings do not qualify for "Eggsaver" shipping and this will be shown in your shopping cart.