I don't imagine that you will find too many people that are able to give you an answer from experience Emma.
I do recall a couple of years back that a woman from the USA I think it was had wanted to immigrate to be with a partner and she had a bit of a battle with immigration because of diabetes, but she eventually got approval.
Health is not an area of immigration that I have paid a lot of attention to other than knowing there are various checks/restrictions on people in respect to high risk countries for TB and Yellow fever etc.
Have you searched
Department of Immigration and Citizenship yourself to see if any restrictions apply re people in remission.
The next step that you have referred to is for health insurance and I am not sure how the various health insurance companies would view the situation, and no doubt their views could be influenced on how long it has been.
I'd suggest that you contact some australian health insurers and
Health Insurance, Private Health Cover, Home & Contents Insurance, Private Health Insurance - Australian Unity is one of the smaller yet progressive companies that may have a friendlier easy to communicate with approach to find out what their policy would be.
A positive outcome in respect to that is more pertinent than attempting to find a sponsor to cover future medical/insurance costs which just restricts employment potential fields, and if you can get health insurance you may find that the cost is not so significant that you cannot cover it yourselves.