While you gather your information for a disability claim you should register for unemployment as the hours you are working isn't really full employment. This will get you and your family a pensioner concession card which has been a huge help to me when my Doctor stopped bulk billing. It also means my $96 a month precriptions only cost me about $15.
Disability works on a points system with about 13 categories. A few points in a few sections may tally the required score but it doesn't mean you immediately get the pension as you need to be registed with a disability job provider for 18 months as well. Thats where the register for unemployment comes in as they can get you that disability job provider.
If you are incapacitated enough in one section and reaches the appropiate score you can get immediate disability pension.
Sometimes you might need a lawyer who specialises in helping your claim or a health worker with appropriate credentials.
I am trying again after I was knocked back in 2017. I haven't worked since breast cancer in 2015. This time I have a whole mental health team helping from the psychiatrist, psychologist and mental health nurse and am waiting on the judgement from Centerlink now.
My husband does work but he is registered as my carer and still gets a little retainer every fortnight and every little bit helps. In unemployment I have to report every fortnight, my income and hours (zero) and my husbands as well. They then pay me, with a reduction in my payment but I do get something at least. I also get subsidies to electricity which is good and our council rates have a pensioner concession too.
Here is a link which is hard to find online with the tables.
https://www.dss.gov.au/sites/default/files/documents/05_2012/dsp_impairment_final_tables.pdf