In 2014/15, a new suite of questions were included in the Household, Income and Labour Dynamics in Australia (HILDA) survey to allow the deprivation approach to measure poverty to be applied. The sample covered 9,538 households, a fully enumerated sample of 23,107 and responding adult sample of 17,512. 
In this survey, respondents were asked from a range of items covering all aspects of life, which items were essential for living in Australia today, which they had or not and for those they didn’t have whether this was because they couldn’t afford it.  The table below shows the percentages regarding each item as essential and for those items seen by a majority as essential, the percentages who lack the item because they couldn’t afford it. the table is sortable by columns.

Item Is it essential Doesn't have, can't afford
Medical treatment when needed 99.7% 1.0%
Warm clothes and bedding, if it’s cold 99.6% 0.1%
A substantial meal at least once a day 99.3% 0.1%
Medicines when prescribed by a doctor 98.9% 0.5%
Dental treatment when needed 97.4% 4.9%
A decent and secure home 96.9% 0.3%
When it is cold, able to keep at least one room of the house adequately warm 95.4% 0.7%
A home with doors and windows that are secure 94.5% 0.6%
A yearly dental check-up for each child 94.4% 3.3%
A roof and gutters that do not leak 86.1% 2.3%
A telephone (landline or mobile) 84.3% 0.1%
A hobby or a regular leisure activity for children 84.1% 3.4%
Furniture in reasonable condition 82.8% 0.3%
Children being able to participate in school trips and school events that cost money 82.2% 0.9%
A separate bed for each child 79.7% 0.8%
Getting together with friends or relatives for a drink or meal at least once a month 79.4% 2.4%
At least $500 in savings for an emergency 79.4% 11.3%
A washing machine 79.1% 0.3%
Home contents insurance 61.7% 7.7%
Comprehensive motor vehicle insurance 59.1% 4.4%
New school clothes for school-age children every year 57.3% 6.7%
A motor vehicle 55.9% 2.0%
In ‘Mapping the Australian Poverty Profile: A Multidimensional Deprivation Approach’, Peter Saunders and Yuvisthi Naidoo analyse this data to find an overall measure of deprivation poverty.  Overall, they found 10.7% of the population was in deprivation poverty.  This overall figure is very similar to the 10.5% in income poverty based on 50% of median income. However, they found that different groups are identified as in poverty using deprivation measures than are found using low income measures. In particular, deprivation poverty shows higher rates the income poverty for all age groups up to the age of 54 while the deprivation rates are lower than the income rates for those older than 54. They conclude:
It is apparent that low income does not always automatically imply that poverty exists, and that a higher income may not guarantee that it does not. The deprivation approach embodies community views about the meaning of poverty that when translated into concrete measures reveal that factors other than income are important in determining whether or not people can achieve an acceptable standard of living, as judged by their peers in the community. This analysis represents a first step in highlighting how different measures of poverty impact on the overall severity of the problem and on the relative positioning of different groups. These differences provide an initial clue to the underlying causal factors and have potentially important policy implications. One important conclusion is that it would be unwise to rely on a single measure like the income poverty rate when the evidence shows so clearly that alternative measures produce different results—at least for some groups. Sensitivity analysis using different poverty lines can improve our understanding but does not address the basic issue that income alone is a limited metric for studying poverty. (Mapping the Australian Poverty Profile: A Multidimensional Deprivation Approach’, Peter Saunders and Yuvisthi Naidoo ).
Saunders and Naidoo also look at the difference in the percentages lacking an item between those who lack it because they say they can’t afford it (‘derived deprivation’) and those who lack an item whether they say they can afford it or not and who also see the item as essential when asked about whether the item is a necessity (inferred deprivation’). They found small differences between the derived and inferred deprivation rates for 12 out of the 22 items where the percentages lacking the item were low (under 3%). There were larger difference when the both the derived and inferred rates were higher, suggesting ‘ suggesting that ‘the response to the affordability question does exert an influence on measured deprivation, possibly due to the nature of the items themselves making it harder for people to differentiate between choice and constraint’.
For full details see: ‘Mapping the Australian Poverty Profile: A Multidimensional Deprivation Approach’, Peter Saunders and Yuvisthi Naidoo, The Australian Economic Review, vol. 51, no. 3, pp. 336–50; DOI: 10.1111/1467-8462.12266. Not open access
A presentation on poverty measurement in Australia was made by Melissa Wong, Social Policy Research Centre, at the Second Peter Townsend Memorial Conference, Measuring Poverty: The State of the Art, in 2011.

The paper reported on research in Australia into perceptions of necessities and lack of necessities.

In 2010, essential items covered:

  1. Warm clothes and bedding, if it’s cold
  2. Medical treatment if needed
  3. Able to buy medicines prescribed by a doctor
  4. A substantial meal at least once a day
  5. Dental treatment if needed
  6. A decent and secure home
  7. Children can participate in school activities and outings
  8. A yearly dental check-up for children
  9. A hobby or leisure activity for children
  10. Up-to-date schoolbooks and new school clothes
  11. A roof and gutters that do not leak
  12. Secure locks on doors and windows
  13. Regular social contact with other people
  14. Furniture in reasonable condition
  15. Heating in at least one room of the house
  16. Up to $500 in savings for an emergency
  17. A separate bed for each child
  18. A washing machine
  19. Home contents insurance
  20. Presents for family or friends at least once a year
  21. Computer skills
  22. Comprehensive motor vehicle insurance
  23. A telephone
  24. A week’s holiday away from home each year