Hi there,
At the NSW BDM online index, there are some baptisms indexed that are obviously associated with indigenous families. These can be found by simply searching with the surname as "Aboriginal", and of course there's other baptisms indexed where either the father's name or the mother's name is recorded as "Aboriginal". It may well be that "your" Elizabeth Smith was not baptised until around the time of her marriage banns, so it could be worthwhile checking the parish records in the district where she married John Bailey.
As a word of caution, though, those Early Church Records (ECR) that the NSW BDM has indexed, were not civil registrations, which commenced post 1856. Not all ECRs were forwarded to the NSW BDM when civil registration commenced, and there are plenty of examples where there are extant parish records for B (baptisms), D (burials) M (marriages) that still have not been passed on to the NSW BDM.
Many of the Parish Records (upon which the ECR's are based) have been microfilmed and are held at (for example) the NSW State Library, in Sydney. Those films have much more details on them than the ECR transcript certificate based on the NSW BDM - for example the film will often have the occupation/ employer /address of the father, or may actually be on the "illegitimate" list.
One of the first rules/regulations that Gov Macquarie introduced (Sept 1810) was the recording of Births and Deaths in the Colony. This was to do with statistical purposes, including calculating feed/grain for the stores to feed the convicts, the convict guards, and others who were dependent on the Govt Stores. Musters, not just of convicts, but "General Musters" were held regularly. Some of those records are still in existance, so perhaps Elizabeth Smith may be named in one or more of those records too
Good luck with your searchings, hope this brief overview helps to advance your own tree.
Cheers, JM
