In November of 1800, Governor King issued a Proclamation concerning the coins that were circulating in the colony at the time. By fixing the value for each coin commonly found in the colony slightly higher than its normal value, Governor King hoped to encourage the coins to be kept within his domain, rather than flowing out through trading ships.
Of course, the Proclamation did little in achieving it's goal - merchants aboard visiting ships simply raised their prices to match the inflated values of the coins.
The next attempt to prevent coinage from leaving our shores was the Holey Dollar and Dump. Governor King's successor, Governor Macquarie, acquired a large shipment of Spanish dollars in 1812, 40,000 Spanish dollars arrived from India on board the Samarang.
But before releasing them for circulation, the dollars were mutilated, following the practice of other British colonial governors in Canada and the West Indies: the centres were punched out, then both the centres (the Dumps) and the ring-shaped Holey Dollars were counterstamped with the colony's name and their new, inflated denomination.
The mutilation made the coins unacceptable to foreign traders, and provided a bonus in that two coins were produced from one, doubling the amount of available coins. This, combined with laws preventing them from leaving the colony, proved much more effective than the earlier Proclamations in keeping coins within the colony. Holey Dollars and Dumps remained in circulation until sufficient British coinage could be supplied to the colony in the 1820's. From that time until 1910, British coins were the primary coins in circulation.
The Gold Rush of the 1850's placed additional strain on the economies of the Australian colonies, with increasing prosperity and increasing population as people flocked to the goldfields from all over the world. Local traders, constantly running out of small change, resorted to producing their own tokens. Even though they're not official coins, they're still considered an important part of our monetary history.
All that gold the diggers were finding wasn't much use to people unless it could be turned into coins. The South Australian government tried to make 1 pound and 5 pound coins for local use, but ran into problems with the bureaucrats back in London. Eventually, a branch of the Royal Mint was opened in Sydney in 1854.
The first gold sovereigns produced by the Sydney mint were unusual: their design was radically different to those being produced in London, with the words "Sydney Mint" and "Australia" featuring prominently and a distinct portrait of Queen Victoria, with wattle (an Australian flower) in her hair. In 1870, the Sydney mint stopped making these distinctive coins; from then on their gold coins looked identical to the ones being made in London, except for a small S for Sydney mintmark. Additional branches of the Royal Mint were opened in Melbourne in 1872 and Perth in 1899.
Not sure how far forward you want to take it (in Australia, the "colonial" period goes right up to 1901) but I hope this helps.