Hi,
Sorry, but I doubt that Maud/Madge was of Aboriginal descent and so I cannot see any reason for Madge needing a Certificate of Exemption. Madge's mum was not a married woman when Madge was born, and Madge's birth is indexed under Madge's mum's then surname of SKINNER.
You may need to contact the NSW State Archives for further information re the issuing of those certificates which I have understood were not part of the administrative system until the mid 1940s ...
https://www.records.nsw.gov.au/series/11 I am not sure if there are public access restrictions on the following NSW archive listings
https://www.records.nsw.gov.au/series/26 covering the Board for the Protection of Aborigines
1916 - 1928 But if you contact NSW State Archives, please do mention that the children were removed from their mum's care following her burn injuries in 1925 and then restored to her in 1928. Although unless Doreen and her siblings' Dad was of Aboriginal descent, I think the children's removal and restoration would more likely be in accordance with the then Child Welfare Act 1923, rather than the Aboriginal Protection Act.
In an earlier post I noted various pointers to NSW bdm certificates of registration for Madge's birth in 1882, her mum (Amy Ann)'s marriages 1888 and 1930, and back to the 1861 marriage of Amy Ann's parents at Braidwood, NSW in 1861. Other RChatters had also included similar sightings, and electoral roll sightings too.
I had noted that Madge's mum was Amy Ann SKINNER, and that Amy Ann SKINNER's parents were Thomas SKINNER and Catherine WELLS. I have not looked for further information on Amy's parents, but I can see a possible brother for Amy. If you were to obtain the official transcription for the birth of Thomas A SKINNER, registered Wellingrove, in 1868, you should be able to find the names and ages of his older siblings, so hopefully it should mention Amy. It is NSW BDM reference #17669.
Here is the 1923 Child Welfare Act
http://classic.austlii.edu.au/au/legis/nsw/num_act/cwa1923n21142/ Here is the 1918 Aboriginal Protection Act
http://classic.austlii.edu.au/au/legis/nsw/num_act/apa1918n7342/ For many decades in NSW children were removed from their mothers under the provisions of the Child Welfare Act. It did not matter what ethnicity for their parents. If Madge was hospitalised and required long term treatment for her burns, then it is quite possible that the children were taken into 'state care' until she had recovered sufficiently for them to be returned to her care. But, in my experience, by returning them to her care is indicating they were not removed under the Aboriginal Protection Act. I may well be wrong, and I am happy to be corrected.
JM