While asylum-seekers and how to deal with them will be high on the agenda, Tony Abbott insists the crucial visit will focus on more than just one issue.
Amanda Cavill reports.
Mr Abbott will meet President Yudhoyono during his overnight visit to Jakarta and says trade will be an important component of the visit, his first overseas trip since becoming Prime Minister.
Related: Chief Political Correspondent Karen Middleton previews the talks set to take place in Jakarta
He's accompanied on the trip by Foreign Minister Julie Bishop, Trade Minister Andrew Robb and about 20 business leaders.
"I want this to be the practice for significant Prime Ministerial trips overseas. I believe these are a great opportunity to showcase Australia and to offer ourselves to the world on a mutually beneficial basis. We will be covering a range of matters because this is an important relationship and it's important to get it right at the start of this new government."
But people-smuggling and Australia's controversial plan to turn back the boats will be front and centre following the death or disappearance of more than 50 asylum-seekers off the coast of Java last week.
Survivors are blaming the Abbott government for the tragedy.
Interim Labor leader Chris Bowen says the new government has made the relationship with Indonesia all about boats and this will be a problem for Mr Abbott .
"I think the relationship needs to be much deeper in terms of trade and investment and economic links and international students, for example, one area that needs a big focus. That is all true and that was the focus of the previous government and would have continued as Kevin Rudd and I had outlined. But unfortunately all of those talks will be overshadowed by the ham-fisted approach of Tony Abbott and Julie Bishop in the last week."
Alexander Downer, who was Foreign Minister in the Howard government, says the issue of asylum-seekers needs to be resolved before economic ties with Indonesia can become a focus.
He says there is a great deal of scope to broaden the economic and trade ties between the two nations.
"The trade relationship is very underdone. Indonesia is our 12th largest trading partner. Even with Malaysia with ten per cent of the population of Indonesia we have more trade. There's very little Australian investment in Indonesia compared to countries like the UK and the US. But clearly there's no point in sweeping under the carpet the issue of boats. That has to be dealt with as well and it clearly will be dealt with. But I think it's important that decisive action is taken quickly to close this trade."
He suggests a scheme similar to Labor's Malaysia solution, where Australia would fly back to Indonesia any asylum-seekers who come on a boat without a visa.
In exchange, Australia would take one UNHCR-approved refugee from Indonesia for every person sent back.
Also on the agenda during Mr Abbott's visit to Indonesia will be live cattle exports.
The live trade from Australia was suspended by the Labor government in 2011 amid animal cruelty allegations.
Greens leader Christine Milne says Mr Abbott and Ms Bishop should also discuss Indonesia's proposal to buy about one million hectares of Australian farmland to raise cattle for beef.
Senator Milne opposes the proposal.
"They have said this is how they think about self sufficiency. Essentially outsourcing food production to Australian land. Well, the Greens oppose the sale of agricultural land in Australia to wholly owned subsidiaries of foreign governments. It is not in our interests to abandon trade and instead sell of our land and water to other countries. So Tony Abbott better raise that issue when he's talking about the whole issue of beef. "
However, Australian farmers support the idea.
They say the number of cattle that could be bred on a million-hectare property would not pose a threat to Australia's live cattle exporters.
Any Indonesian purchase of Australian land must be approved by the Foreign Investment Review Board and could also be blocked by the federal government.
