Absolutely no way that QANTAS would be self insured. It is possible, but improbable, that they would self insure Personal Accident to employees, baggage claims and/or Loss of Licence insurance but even this is most likely covered in the Australian domestic market.
QANTAS hulls, liabilities and third party cover will be underwritten and re-insured on the world wide insurance market, as is usually the case with any airline of a reasonable size.