Australian Prime Minister Julia Gillard vowed to stand firm on her controversial carbon tax plans Monday despite the first poll since the levy was announced showing support for her Labor party plunging.

Gillard unveiled a tax on the nation's top 500 polluters a week ago in a bid to reduce carbon emissions blamed for global warming, starting July 1 next year.

But it has only intensified the unpopularity of the country's first female leader with support for her and the government at record lows in a new Nielsen poll published in the Sydney Morning Herald.

The poll of 1,400 voters has the conservative opposition leading 61 percent to 39 percent in a head-to-head race -- an 11-point swing against the government since Gillard wrested power last August by ousting Kevin Rudd.

Labor's primary, or first preference, vote, taking into account all parties, stands at just 26 percent -- the lowest level for any major party in the poll's history, while just a third of voters approve of Gillard's leadership.

Despite Gillard launching an election-style roadshow to sell the carbon tax's merits to a sceptical public, blitzing television and radio across the nation, 53 percent of respondents felt they would be worse off.

Pollster John Stirton described the results as "diabolical" for Labor, but Gillard insisted she would not bow to the pressure.

"I've well and truly got the courage of my convictions and I will be out there providing the leadership necessary as we tackle this big reform," she told reporters.

"It's actually about showing the leadership that is necessary for the country's future and that's what I'm doing."

Australia is one of the world's worst per capita polluters due to its reliance on mining exports and coal-fired power.

But business leaders have said the levy will not only cost taxpayers billions and force major industry to slash production and jobs, but will fail to reduce global carbon emissions.

While the polls were disastrous, Gillard at least won support Monday from the country's largest union for her plan to price carbon.

The Australian Workers' Union said it believed the government had developed a package that ensured jobs would not be lost.

"We said quite rightly and quite proudly that our union would not support a price on carbon that costs the jobs of our members. We hold that position today," union national secretary Paul Howes told reporters.

"But we believe that the government has delivered a package which addressed the concerns we have."

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