The prime minister has a 28-point lead as preferred leader among women, but that drops to a 14-point lead among men.
Her government leads Tony Abbott's opposition 58-42 per cent among women, but the vote is tied 50-50 among men.
The poll shows Labor's two-party vote up two points in a fortnight, while its primary vote, on 42 per cent, has risen three points, to move ahead of the opposition.
The coalition primary vote is down one point to 41 per cent.
The Age says in Queensland, where the government is defending 10 marginal seats, and Western Australia, Labor is trailing 46-54 per cent on the two-party vote.
On the figures in recent Nielsen polls, the government could lose most or all of its Queensland marginals but it would also pick up seats in other states.
On the basis of the poll of 1400 people, taken from Tuesday to Thursday, the government would get a swing of about one per cent from the 2007 election and increase its majority.
