How does an idea or recommendation from a government department become a bill and how do resources get allocated to the government department? How long does this process take?
Thank you for your question, Lucinda! Government departments communicate directly with the minister responsible for their department. The minister might choose to present an idea from the department to Cabinet for discussion. If Cabinet agrees to the idea, a bill – a proposed law – is drafted, and the minister introduces that bill to the Parliament. Resources are allocated by the government to the department and are explained in the Budget papers each year. Budget bills are considered by the Parliament and must be agreed to before resources can be allocated.
The process of making and passing a bill depends on how complicated, urgent or controversial a bill is. In the event of an emergency a bill can pass in a day. However it is more usual for it to take weeks or months in order to give the Parliament time to consider the bill carefully.
Federal Budget process.

Parliamentary Education Office (peo.gov.au)
Description
This diagram illustrates the development and operation of the Budget. Budget documents are prepared by the Treasurer and introduced through a speech to the House of Representatives. Members of parliament examine the Budget bills. The Senate examines the use of the Budget throughout the year in Senate estimates committees.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
You are free to share – to copy, distribute and transmit the work.
Attribution – you must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
Non-commercial – you may not use this work for commercial purposes.
No derivative works – you may not alter, transform, or build upon this work.
Waiver – any of the above conditions can be waived if you get permission from the copyright holder.