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.
Actually they are self insured in the above areas. That is why they introduced the 'Be Safe' program, it is used within the whole group including Boston Bruce's love child Latestar. It is a cheaper option.
However I am uncertain as to what extent 'self insurance' reaches in the instance of a hull loss or something like the Dugong occurence in Singapore, but certainly eveything else is covered by self insurance.
Who knows, maybe 'da little fella' also has his monthly bonus and shareholder options insured also ??