The American declaration of independence is considered a big deal in the founding of the country. When other countries divide or separate do they have declarations of independence and are they considered sacred documents to the peoples of that country?
There was no "declaration of independence" when the Australian colonies decided to federate and become an independent country. There were a few semi-famous speeches, like 'The Tenterfield Oration', and there was some literature on the subject. However, the emphasis of most speeches and articles was "The colonies must be united!" rather than "Independence from Britain!"
Our great big document was a bill passed peacefully and without major controversy by the British Parliament: the Commonwealth of Australian Constitution Act of 1900. That's our Constitution. That's our "sacred document", such as it is. Most modern Australians are aware that it exists, but couldn't tell you what it says even in the broadest terms.
As direct comparison to the US you have countries like Canada that got independence from the UK. Many became dominions (essentially independent domestically but dependent internationally) in the later 19th century, through getting agreement locally and in UK, and then got more independence in the inter war period - specifically the statute of Westminster.