There is currently a gun amnesty run by the federal government.
- What motivated the gun amnesty?
- Who motivated it?
- What is the objective?
- Is it likely to achieve the objective?
- How much is it likely to cost?
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There's also a National Firearms Amnesty 2017 site set up by the government that includes information regarding the amnesty.
The site mentions that the aim is to reduce the number of unregistered firearms in the country:
Why is the amnesty being held?
The aim of the amnesty is to improve public safety by reducing the number of unregistered firearms in Australia. The Australian Criminal Intelligence Commission estimates there are more than 260,000 firearms in Australia's illicit firearms market. The use and movement of illicit market firearms is a national problem; the amnesty is one of several initiatives being used to address firearm-related crimes and threats.
It's unclear how successful this year's gun amnesty will be. However, a previous gun amnesty, which was carried out in 1996, allowed the government to buy back almost 700,000 newly outlawed guns though the one in 1996 was for guns that were outlawed after gun reforms. So, since the conditions are different, it isn't a good comparison. (Thanks @Brythan for pointing out)
As for cost, it's still too early to tell at the moment as the government didn't seem to provide any estimate.