A free site provided by The National Library of Australia and which contains digitised newspapers among many other items of interest.
Highly recommended if researching family who have emigrated to Australia.
Trove Historical Newspapers. Free. Extensive range of newspapers digitised and easy to search.
Will show a list of children or marriages etc. For births will only show results from more than 100 years ago.
Will show whether born in City or country. (Other States will have this facility as well)
On the page will be a sub heading "Tasmanian Names Index" Input a name and you will see all the documents relating to this person which have been digitised.
Also on this site are historical maps and photographs including some convicts
This site has extensive records.