In a speech to the institute, Gillard was careful to separate politics from the conduct of the war and the timetable for withdrawal, but it was clear she expected Australia's 1550 troops to begin leaving by mid-2013, with most home by the end of the year.
Previous timetables had placed the deadline at the end of 2014.
Opposition leader Tony Abbott cautiously welcomed the prospect of Diggers coming home sooner but said he wanted to believe they would return with "success rather than failure under their belts".
New Greens leader Christine Milne urged an immediate start to withdrawal.
Gillard's speech came ahead of two key meetings - International Security Assistance Force foreign and defence ministers in Brussels this week, and a leaders' summit in Chicago next month - which will be central to Australia's plans.
It also came after Taleban attacks that killed more than 50 people.
"These attacks were successfully countered by the Afghan national security forces without substantial direct support from ISAF forces in Kabul," she said.
Gillard's argument for early withdrawal was supported heavily by claims of significant progress in military, development, governance and political strategies that she said underlined the success of continuing transition to Afghan control of the country.
She said Australia's consistency of purpose in Afghanistan "must not be mistaken for persistence in a strategy which is not working".
Security gains in the past 18 months had included the death of Osama bin Laden, the death or capture of most of al-Qaeda's senior leaders and the retreat of survivors to the border with Pakistan. Gains in some areas were fragile and not beyond reversal, but insurgent attacks had decreased every month since May last year, and Afghan forces now led more than a quarter of special operations and just under half of conventional operations.
About half of the population now lived in areas in which Afghan forces had begun taking over responsibility for security.
Life expectancy since 2001 had increased by five years to 48, access to basic healthcare had grown from 10 per cent of the population to 85 per cent, and more than seven million children, including 2.5 million girls, were now enrolled in school. In Uruzgan Province, Australia's main base of operations, the 4th Afghan Army brigade trained by Diggers was steadily taking over, and Gillard said she expected President Hamid Karzai to name areas for transition in the next few months.
"Once started, this should take 12 to 18 months. And when this is complete, Australia's commitment in Afghanistan will look very different to that we have today.
"We will have completed our training and mentoring mission, we will no longer be conducting routine frontline operations, the Provincial Reconstruction Team will have completed its work and the majority of our troops will have returned home."
But she warned: "Conditions on the ground will determine the timetable for transition. People will not see Australian soldiers come home on the first day of transition."
Gillard also said that after the main force of foreign troops left, support would still be needed and she would emphasise in Chicago that Australia would pay its fair share. This included niche training in areas such as artillery, policing and a limited special forces presence "in the right circumstances and under the right mandate".
Gillard also hopes to sign a new development agreement with Karzai, covering electoral processes, security, trade and investment.
"We did not enter this conflict lightly and we do not persist in it without great care. This is a war with a purpose. This is a war with an end. We have a strategy, a mission, and a time frame for achieving it."
