Kevin Rudd in Beijing.
Prime Minister Julia Gillard will have to navigate a nuclear power crisis in Japan and a nuclear weapons crisis on the Korean Peninsula, but her diplomatic dexterity will not be tested until she gets to China.
Japan and South Korea are more important to Australia than is often recognised, given they are Australia's second and third-ranking export markets and also important security partners. But China now towers above them on the economic charts - buying a quarter of all Australian exports - and plays an increasingly central role in all the major global challenges.
And the China relationship is much, much more difficult to get right. Given how much is at stake, it is surprising that no Australian prime minister has visited China in more than three years - excluding Kevin Rudd's visit alongside more than 80 other world leaders during the 2008 Olympics.
Mr Rudd was not comfortable with the domestic debate on China and he found himself in serious disputes with Beijing over investment, military postures, human rights (especially in Tibet and Xinjiang) and the detention of Australian citizens.
Tensions came to a head in mid-2009, with the arrest of Australian iron ore salesman Stern Hu and the visit to Australia of Uighur leader Rebiya Kadeer, until the Chinese leadership took steps to hose things down.
Chinese officials hope to draw a line under the Rudd era and form a stronger bond with Ms Gillard. But none of the old bilateral problems have gone away and some are getting more difficult.
China is in the midst of its broadest and most brutal political crackdown on civil society in more than 20 years, excluding its repression in Tibet and Xinjiang. Australian business people remain in detention, with at least one in legal limbo.
And, from the Chinese point of view, Ms Gillard's recent trip to Washington showed a worrying willingness to be drawn more tightly under the US security umbrella.
''I personally am extremely concerned Australia could be leaning even closer to America,'' said a Chinese official who has been working on Ms Gillard's trip. ''If this is so, the relationship between Australia and China will continue to be economically intimate but politically tense.''
Ms Gillard does not yet claim to have a firm grip on global diplomacy and she has been to China only once, more than a decade ago. She has no ambition to achieve a bilateral ''breakthrough'' but she will highlight the strength of economic ties and press for modest progress on trade, investment and climate change. Trade Minister Craig Emerson and Health Minister Nicola Roxon were in Beijing yesterday.
Analysts in Australia and China will be looking for Ms Gillard to formulate and clearly enunciate a sustainable position on all the sticking points, including Chinese investment, human rights, detained Australian citizens and military and security questions.
After symbolic visits to tsunami-ravaged Japan and war memorials in South Korea, however, it may be enough if Ms Gillard establishes some rapport with Chinese leaders, gets a feel for how the country works and leaves without making mistakes.
John Garnaut is Fairfax China correspondent.