If in Oz, ordering serum vials from a US internet supplier is suspect in itself (reason - why wouldn't you just order them from your own country). Further, any price advantage is usually negated by the added freight and custom costs.
You most probably wont have to provide ID to purchase the vials, however, you will need to provide ID to get the package through Oz customs. Further, vials would be watched as they usually contain performance enhancing drugs or other contrabans. Even though they will be empty (once the package is opened); it creates a 'flag' against your name during subsequent imports.
A false or old ID wont work either, they will verify the delivery and home address of the consignee. Or they will simply hold onto it until YOU contact them regarding the whereabouts.
That said, if you have nothing to hide and the vials are put to legitimate use; you have nothing to worry about. But as that most probably isn't the case, your best bet would be to make up a good story and order them locally. The good news is you dont have to hassle your dreaded chem supply house, you can order them from specialist science supply companies. They are easy to google...
Then you need to order, pay and take delivery as anonymously as possible. It can be done (UTFSE)