6 Postal prepayment impressions, franking machine impressions and
impressions made by a printing press or another printing or stamping process
in accordance with the Acts of the Union may be used only with the authorization of the member country or territory
That would cover the Auspost printed labels as “authorization by the member country” ie Australia.
Further to this is:
"(Convention Manual – Art. 6; Prot. Art. II; Art. 06-001 Volume I – 11)
Article 06-001
Prepayment. Methods of denoting prepayment
1 Letter-post items
1.1 As a general rule, letter-post items shall be fully prepaid by the sender.
1.2 Methods of denoting prepayment
1.2.1 Prepayment shall be denoted by means of any one of the following methods:
1.2.1.1 postage stamps printed on or affixed to the items and valid in the member country of origin;
1.2.1.2 postal prepayment impressions valid in the member country of origin and dispensed by automatic vending machines installed by designated operators of origin;
1.2.1.3 impressions of officially approved franking machines valid in the country of origin, operating under the direct supervision of the designated operator of origin;
1.2.1.4 impressions made by a printing press or other printing or stamping process when such a system is authorized by the regulations of the designated operator of origin.[my highlight]
2 Letter-post items may also be provided with an indication that full postage has been prepaid, for example, “Taxe perçue” (“Postage paid”). This indication shall appear in the top right-hand part of the address side and be authenticated by a date-stamp impression of the office of origin. In the case of unpaid or underpaid items, the impression of the office which prepaid the item or made up the postage on it shall be applied opposite this indication.
3 Parcels shall be prepaid by means of postage stamps or by any other method authorized by the regulations adopted by the country of origin or by its designated operators."
Though 1.2.1.3 could also be an applicable section, depending on whether the printers used by Auspost are considered for this section to be Franking Machines, they may have this as part of their designation in Auspost.
EDIT: Auspost rules forbid using both stamps and label on the same item. Auspost enquiry confirmed this is the case.