No, it doesn't work that way.
To be passed into law, a Bill must be passed by both Houses of Parliament, the House or Representatives, and the Senate. Together, these constitute the Parliament of Australia. The Bill must then receive Royal Assent. Only then does the "Bill" become an "Act of Parliament" - a law.
First, a law must be proposed - a draft Act of Parliament. In has no legal standing yet.
That is called a "Bill".
A "Bill" only becomes an Act of Parliament - a law - when it has been passed by both Houses of Parliament and has received assent form the Governor-General.
It works this way:
Normally the Minister responsible gives written notice to the House of Representatives that he/she will propose a Bill, for whatever purpose.
The next sitting day of the House, the Bill is read for the first time, and is available for all members, and the public, to see.
Normally immediately after this, the Minister moves that the Bill be read a second time, and then makes a speech explaining all the details to the House. After that, debate is deferred to give Members time to study the Bill, and to allow for public discussion and reaction.
One option during the process is for the Bill to be referred to a committee to gather information, evidence, witnesses, etc, as it sees it - but the committee cannot change the Bill. The committee can then make recommendations to the House.
This is where the new proposed Citizenship Bill is right now - the second reading (in the House of Representatives) has been moved, but the second reading debate hasn't happened yet.
Then, some (often considerable) time later, there is the second reading debate. The opposition and other Members have their say. After that, there is a vote by the House to establish whether the Bill can be read a second time. If the House approves, that effectively signifies the second reading of the Bill is complete.
After this, the Bill may or may not be considered in detail, depending on Members. The third reading of the Bill, after this point, is pretty much just a formality.
After the Bill is passed, it goes to the Senate - three readings there too. The Senate can agree, or send the bill back to House with proposed changes. These may be agreed to or not, and there may be some communication between the two Houses about this at that time. If the Bill doesn't get agreement by both Houses, it may be laid aside (effectively, dropped) unless it's something imperative like a Supply Bill. Then, there can be a double dissolution and a fresh election.
When a Bill has passed both Houses in identical form, it becomes law after it is presented to the Governor-General and gets his/her assent - whether starting from that date, or retrospectively, or from a future date.
It's important to understand that Labor and the Greens have signified they will not pass the law in its present form - to pass the law, there would either need to be changes, or the Government will need to get votes form the cross-bench in the Senate so it can get the numbers to pass the Bill there.
kaju