To seek better/stronger competition.
Also it was probably to have a better opportunity at qualifying for the World Cup.
At the time they requested the move to AFC (2005) the Aussies had to qualify for the World Cup through a playoff against a team from another region. And they were continuously denied entry after losing those playoffs...
1985, lost playoff to Scotland 0-2, 0-0
1989 knocked out by Isreal who were at the time an OFC country (political reasons).
1993, lost playoff to Argentina 0-1, 1-1
1997, lost playoff to Iran 0-0, 2-2 (away goals)
2001, lost playoff to Uruguay 1-0, 0-3
Many suggested that Australia should abandon OFC and go to AFC where qualification for the World Cup would appear to be easier. The Australian FA had tried to join AFC in the past but were always refused. But in March 2005 FIFA apparently stepped in and helped arrange the Aussies into AFC.
Later that year Australia defeated Uruguay on penalties to secure a World Cup berth in Germany 2006. By the time the World Cup began Australia were officially members of AFC but during the tournament they were deemed to be representatives of OFC until their run in Germany was over.