One of the quotes you will have to get is for travel insurance. If the doctor says that she can travel, you then need insurance as being stranded mid-trip with a medical problem could be tricky. The airline may request that too. Routing will be dependent on cost and final destination. If it's SYD that gives you numerous options.
You would have to be business class as a minimum, which includes the companion. If she can rest horizontal for most of the flights, that would help a great deal.