JLT are the brokers in London, it's not placed with JLT in Australia and the insurers are a panel of well known and established aviation insurance companies based in France, the UK and elsewhere in the world. All aircraft if the Qantas fleet are insured and all are subject to an excess. Excess varies according to type. Jet aircraft have what is called Deductible Insurance which lowers the excess to $100,000.
Qantas will claim on their insurers and they in turn will seek recovery from the ground handler's insurers subject to the limitations of the Ground Handling Agreement in place. Lawyers will be involved and it will go on for years.