How did they trade?
Australia's currency heritage

Many forms of currency were used in the Australian colonies after the arrival of the first European settlers in 1788. In the rough early conditions barter was necessary, and payment in commodities like rum sometimes replaced money in transactions. Some of the first official notes used in Australia were Police Fund Notes, issued by the Bank of New South Wales in 1816.

The Bank of New South Wales was founded in Sydney as the first bank in Australia on 8 April 1817 by Governor Lachlan Macquarie. Branches were initially restricted to the colony of New South Wales, but were later opened at Moreton Bay, Brisbane, in 1850, Victoria in 1851, New Zealand in 1861, South Australia in 1877, Western Australia in 1883, Fiji in 1901, and Papua New Guinea and Tasmania in 1910. In 1982, the Bank of New South Wales merged with the Commercial Bank of Australia to form the Westpac Banking Corporation, which derived its name from from the fact that its major operations are in the Western Pacific. (source: today.wmit.net - April 8)

Addendum:

That bank had an official predecessor. The initial settlement in 1788 was accompanied by a Commissary - a quasi-military officer appointed by the Treasury to provide support. The Commissary had the Military Chest (containing currency) and also the ability to raise bills payable against the Treasury. This enabled the colony to buy currency, pay its employees and purchase supplies and transport. As the colony developed, the Commissariat Store bought and sold produce, hired transport and ships, financed buildings and so on.

The Commissariat provided what were effectively banking services, and though not call a bank, it effectively was one, establishing branches in each town and outpost as required.

Commissariat Stores

When the convict colony of New South Wales was established in 1788, supplies of food and other goods were to be provided to the colonists - the convicts and their gaolers alike - from a Commissariat store. This was an arm of the civil administration responsible for the supply of goods to colonial establishments within the British Empire.

The Commissariat held a strategic role in the economy of the early colony. Its function was to supply and store foodstuffs and other necessities - including liquor, hardware and other goods - for the population. Though this role diminished over time, it was significant within both Sydney Town and the colony for many decades.

In the early years, the Commissariat was the only buyer available for the produce of the colony. And because it had access to credit in Britain, via the use of Treasury Bills to pay for overseas purchases, it was an important avenue of finance. This was later important for the development of commerce, banking and even agriculture in the colony.

Due to the initial lack of ready cash in the colony, and the high credit rating of the Commissariat, its store receipts and bills of exchange were used as currency for many years, until the introduction of enough circulating cash in the form of the  holey dollar  and the  dump . As a result, the Commissariat played a very significant role in the development of the colonial economy as it moved from a convict to a market system.

The first Commissariat building was probably designed in 1809 and built c1810. Under Governor Macquarie a second Commissariat store was built in 1812, as part of the rearrangement of the store s function and role, and was completed just before changes to the organisation and running of the Commissariat occurred. These changes took control from the Governor and placed it with the Lords Commissioners of the Treasury in London, as part of the army commissariat.

But by 1815 the role of the Commissariat was again changing, and Macquarie abolished the custom of supplying the needs of the inhabitants from the Commissariat on credit. This protected the government from a large number of bad debts, and Macquarie felt that  All their wants may now be fully supplied by the Free Merchant Shipping, frequenting this port from England and other countries .
The first Commissariat Store was a U-shaped building constructed on the western shoreline of Sydney Cove. The 1812 building was constructed to the west of the first, next to George Street.
Now let's pose a question.  If the commissariat store handled the financial transactions, did Robert steal the pig because they did not get paid for some of the services from their shipping business on the Hawkesbury?      Effectively there was no currency, but it seemed to be more of a barter system.
Question No2.  How did Robert get his reprieve?  Where are the records?
A call to an Archiver at the NSW Archives confirmed that the Governor had to issue the reprieve, and that would have been instigated from a petition written to him.
It would seem very likely that Elizabeth wrote such a petition.  However, some of the very early records have been destroyed, particularly those prior to 1826.  Many of these early records are incomplete, and many were destroyed in the Rum Rebellion.  There are records in NSW Archives relating to the Criminal Court of the day, which can be searched. However it is highly likely that if there are no records on the current online index, that there are simply no records.
There is also suggestions that there was another Elizabeth Bradshaw in the Colony.
Extensive searching of the available shipping records and online data bases, has not revealed that information.  It has been alluded to on the internet  that a Captain John Bradshaw who served in the Indian Forces,  travelled by boat to Sydney in 1802, with his wife Elizabeth and three children.  The person who supplied that information had him intermingled with Thomas Bradshaw's status.

If this Elizabeth Bradshaw and her husband arrived and settled in Sydney, then she would not have been able to own land, but her husband would.  Unfortunately there are no records which can be sourced to confirm this person, although research is ongoing.  Plenty of Bradshaws were sent to Australia, many of them convicts, but the only Bradshaw in the time frame of the research with this family is Thomas.