The British Constitution is the origin of this rule and the House of Lords has similar limitations regarding money bills.
Historically, this rule was especially important in the UK to prevent the monarchy from controlling how the people’s money was spent. In Australia, the same logic can be applied. It could be said that preventing the Senate from controlling public spending allows that power to remain with the people, rather than the states.
More information on the thinking behind the different sections of the Australian Constitution can be found in Quick and Garran’s Annotated Constitution of the Australian Commonwealth.