Hi Dyuti,
Sorry to hear about your recent loss.
I have already done the Amazing Australia trip a couple of years ago now. I did it with a Singapore stop over and New Zealand add on afterwards. I thought it best to get down under ticked off and done in one swoop as the distance is considerable.
Now Qantas fly via Dubia instead of Singapore why don't you add it as an extra as it cuts the long flying time down considerably. I have been to Dubia years ago but it is more of an attraction place now so there will be lots to do. Agiain JY will have a representative in Dubia to meet you and excursions for you on your stop over. After your stay continue onwards to Australia. Your stop over break again will make the flying that distance not to bad.
If you can afford it I would recommend upgrading to Business class through JY. I did it both ways, you then have a seat that transforms into a bed. My trip home from Christchurch, NZ via Sydney and Singapore was done totally in Business class. Did not find coming back so bad, except for our delay in Singapore due to technical issue with aircraft.
Hope you will consider it, as states - Amazing Australia. Trip of a lifetime.
Best wishes
Eric