As frustrating and annoying the experience might be, I suggest getting any lawyers involved would be counter-productive. Qantas' lawyers would be bigger and uglier than yours, and Qantas has deeper pockets and time on their side.
It would help to know the extent of your comms with Qantas - did you ask for other compensation and re-imbursement beyond the medical costs, which it looks have been covered? Did they say flat no to what you asked for, or you just thought the offer inadequate? Did you get beyond the general response level of person, or did it get escalated to more senior levels? How high?
Not saying you might have done anything wrong in your approach, but advice here will largely depend on what you have already done.
There have been a number of threads here about QF offer of compensation for various issues, nearly all thought to be woefully inadequate.
The company rep here RedRoo I understand has helped to get satisfactory resolution in a number of such cases. if RR doesn't pick up this thread, you can PM them, put your case and ask for assistance. Just state the facts dispassionately about what happened, what QF's response(s) have been to date and what additional compensation you are seeking.
If its not something RR can help with or it seems to be going nowhere I would call to make an appointment with whoever senior you can find in Qantas. When I had a problem - not nearly as serious as yours - I got to see the State Manager, but Tasmania's a much smaller pond than ... what's BDG - Java? I never rely on e-mails when I really want an issue resolved properly.
If at the end of the day you make what you think is a just claim, and are unhappy with the response, while staying reasonable, I wouldn't hesitate to go to the 'Small claims' type tribunal in your state (again, depends if you are Australian resident).
