The latest Newspoll published in The Australian newspaper on Monday shows the coalition has a 51-49 lead over Labor in the two-party preferred stakes.
Labor's primary vote is languishing at 31, compared to the coalition's 38, the poll found.
Some 53 per cent of those surveyed believed the Albanese government did not deserve to be re-elected, while 34 per cent were happy to give it another term.
About 45 per cent believed Prime Minister Anthony Albanese would be the better PM, compared to Mr Dutton's 40 per cent.
The poll surveyed 1244 voters nationally last week.
Meanwhile, modelling from pollster YouGov projected the coalition to win 73 seats at the election - putting Mr Dutton in pole position to form government.
The former Queensland police officer on Sunday was spruiking a pledge to upgrade public lighting to improve safety in a suburb outside Darwin where youth crime is a key concern for voters.
"Part of our plan to get Australia back on track is about keeping Australia safe - safe for families, safe for businesses and safe for communities," he said.
The former coalition hard man has softened his image since ascending to the leadership but crime and border security are still his bread and butter.Â
Polls show voters consider Mr Dutton a stronger leader on matters of law and order than Mr Albanese, who voters consider the weakest party leader in decades.
The announcement coincided with another opportunity to whack Labor for being weak on borders.
As Mr Dutton fielded questions from reporters in Palmerston, Home Affairs Minister Tony Burke revealed a deal had been struck with Nauru to resettle three non-citizens following the NZYQ High Court case.
Australia will pay Nauru to take the trio which includes a convicted murderer.
Mr Dutton said Labor's "mess" at the borders was increasing boat arrivals.
He said the Albanese government had cut back aerial surveillance by 20 per cent, and on-water surveillance has been reduced.
While these issues are Mr Dutton's strong suit, Redbridge polling published in News Corp papers on Sunday showed they are not the most pressing for voters.
The cost of living was far and above the biggest concern, with 84 per cent of respondents ranking it in their top three.
However Mr Dutton has vowed not to support electricity subsidies for Australian families, ruling out an extension to the government's energy bill payments because he claims they are contributing to inflation.
Housing Minister Clare O'Neil said that showed his hypocrisy "knows no bounds".
"Every opportunity, we're finding ways to try to provide assistance to people, and in almost every instance, Peter Dutton has stood in our path," she told Sky News.
