The allied victory in the war to disarm Iraq by removing its dictator is an extraordinary feat of arms, and the destruction of Saddam Hussein's statues in Baghdad now matches the destruction of the Berlin Wall in 1989 in the iconography of freedom. But the achievement will only be worth the lives lost if a new form of government emerges that is based on the rule of law and the ballot box. The cynical exponents of a faux realpolitik are already beginning to explain why this cannot be done, just as they explained three weeks ago how the Iraqi military would stand and fight, and how the patriotic people of Baghdad would rally to defend Hussein's fascist dictatorship. They were proved wrong with great speed as the allied forces took three weeks to the day to win a spectacular victory. Proving the critics wrong by winning the peace will take longer. The challenges faced in the short term by the US and its allies, the United Nations, and, down the decades, by the people of Iraq are profound. Iraq has no experience of democracy, although it does have strong traditions in education, science and the arts. Its government has been gutted by a fascist regime which used the resources of the state to reward its supporters and punish opponents. Its oil wealth has been squandered for three decades on a dictator's whim. And the nation is divided on lines of faith and ethnicity. Sunni and Shi'ite Muslims do not trust each other and only come together in their antipathy towards the Kurds' ambitions for a homeland. These are all problems which only the Iraqis can solve over time, through a stable and ultimately democratically sanctioned form of government.

In the immediate term the task for the allied armies is to establish the rule of law wherever their writ extends, to end the looting, and to prevent mob justice against the Baath party functionaries now nervously facing their victims. They must restore basic infrastructure and ensure food and medical aid, and they must begin to lay the foundations for a government of Iraq for and by the people. Having ducked the war, the Europeans, notably the French, now want to dictate the peace, and demand a driving role for the UN. Certainly, there must be a role for the UN, mainly in the administration of aid programs. But there is no case for the Security Council, the body which could not unite to confront Hussein, to be trusted with the task of designing a government to replace the dictatorship. The Americans and British spent the blood and treasure to win this necessary war and they must take on the responsibility to manage the peace. Australia has a similar obligation and the Prime Minister's announcement yesterday that we will provide staff for the transition administration, and a limited military presence, is appropriate.

But not for long. The war was fought to disarm and destroy a dictatorship, and from the beginning of the peace it must be made clear to the people of Iraq and the wider Muslim world that the allies will leave Iraq as soon as a legitimate and viable government can be established. There is no doubt that this is exactly what the US will do. As President George W. Bush put it earlier this week, "Iraqis are plenty capable of running Iraq". America's enemies may not like to hear it, but the US has no imperial tradition. After World War II it rebuilt the Japanese and German economies, helped establish democracy in both countries – and then went home.

"The thirst for freedom is unquenchable" is how White House spokesman Ari Fleischer summarised the scenes on the streets of Baghdad yesterday: like much of what the current US administration says, it is both corny, and utterly true. What the scenes in Baghdad and Basra confirm is that, once liberated from a reign of terror, people in Iraq, like people everywhere, will choose freedom over tyranny. While some Western intellectuals continue to insist that the "imposition" of democracy upon countries with different traditions is not "appropriate", this is a piece of moral relativism that appears to have escaped the dancing crowds in Baghdad.

It is the people of Iraq who are the first and most important beneficiaries of the allied actions of the past three weeks: after a transitional period, their fate will at last be in their own hands. But there are also significant gains for the people of the wider Middle East. The "explosion" of the Arab street that many predicted has not taken place: there has been some simmering resentment, but even this will be doused by the scenes of rejoicing Iraqis. Luckily, fears that other states in the region would interpret the allied campaign against Iraq as a "war on Islam" have proved, like so much else, delusions of Western intellectuals opposed to the campaign. Rather than producing violence, there is hope that the liberation of Iraq may produce a new impetus for peace between Israel and the Palestinians, by replacing a destabilising influence in the region with a democratic one. The next task for Mr Bush is to resume the "roadmap towards peace" he believes can end the Israel-Palestinian conflict within two years, and produce an independent Palestinian state. For this to happen, however, Israel's neighbours will need to put aside their half century's worth of resentment that Israel exists in the first place. At the same time, there must be a Palestinian ceasefire, and an Israeli withdrawal from Palestinian cities.

There is no emerging evidence of the "hundreds of Osama bin Ladens" that we were warned the confronting of Hussein would spawn. Given the massive disincentive to sponsoring terrorism that Hussein's example will now constitute, the terrorists who are still out there must be starting to have a sense of the walls closing in. Along with Hussein and the Baath hierarchy, they are the big losers out of the past three weeks, along with all the other regimes that rule by terror and fear.

But also among the losers is the UN. How long would these scenes of rejoicing have been delayed if the UN, and those such as France who encouraged its folly, had had their way? How many torture victims were to be sacrificed on the altar of "international law"? As for those in the West who militated against this war, claiming it was illegal and immoral, that it would inflame hatred, and would end up simply replacing one tyranny with another: let them go and tell that to the people of Baghdad. Now they have turned to carping about "where are the WMDs?", as if soldiers who have just succeeded in a near-impossible military task are to be faulted for not having undertaken a systematic weapons inspection process as well.

This was a just war, and one that will make the world a better and safer place. The Prime Minister was not prepared to use what he called the "V" words yesterday, but we will use one of them: Australia's decision to join the campaign is vindicated.