The opposition leader toured one of the state's most important wine producing regions on Thursday, located in the ultra-marginal seat of Lyons which is held by retiring Labor MP Brian Mitchell.
Visiting the Bremley Vineyard in Campania, a town outside of Hobart, Mr Dutton raised a glass of Pinot Noir with two of his three children Rebecca and Tom.
"My favourite wine is probably Shiraz, followed by Chardonnay, Sauv Blanc ... I don't discriminate," he joked.
Standing alongside his deputy Sussan Ley, and his local candidate Susie Bower, the opposition leader spruiked the coalition's previously announced promise of $150 million for an irrigation scheme to supply water to farmers.
Mr Dutton was driven by Ms Bower to his 14th petrol station stop of the election campaign, filling up the car in Sorell while flanked by Liberal Party supporters.
The opposition leader earlier visited CatholicCare Tasmania in Hobart's northern suburb of New Town, located in Clark, one of the safest seats in the country.
It is held by independent MP Andrew Wilkie.
Mr Dutton spoke with CatholicCare Tasmania chief executive Julia Mangan about his pledge of $90 million to address the scourge of domestic violence.
She said there had been a 24 per cent rise over the last year in support provided to people experiencing domestic violence, particularly to women and children.
"Enough is enough," she told Mr Dutton.
"It's past the point of worrying about upsetting certain people."
Under the coalition's proposed changes, using a mobile phone or computer to harm intimate partners would be illegal under new domestic violence offences that would be created if the opposition wins the May 3 election.
The proposal would criminalise the tracking of victims or coercion using the devices, and would attract tough bail laws.
A national register allowing police across the country and other authorities to access and share information about a person's previous family violence convictions to better manage risk would be set up.
Mr Dutton said people needed to make sure they didn't walk past examples of violence in either the workplace or community.
"Australian men have to be the best role models that they can be, and we have to provide an example to our children, in particular, our sons," he said.
"I want Australian men and Australian women to understand and to hear a very clear message from us: that we're absolutely determined to work in good faith to see the best possible outcomes here."
Women and children fleeing family violence would still be supported through emergency payments of up to $5000 through the established leaving violence program.
The Albanese government committed $925.2 million over five years to make permanent the payments, which were available under an escaping violence program trial funded by the previous coalition government.
Following the press conference, six environmental protesters from the Bob Brown Foundation were chanting outside CatholicCare.
"Our climate is under attack. What do we do? Stand up, fight back," they yelled.
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