The CEO was taken aback to find a cot in the room.

"He was surprised, but not in a bad way," Ms O'Dwyer told Fairfax Media, adding the two even had a photo taken in front of the cot, so he could demonstrate the set-up to his organisation.

For Ms O'Dwyer, the first cabinet minister to have a baby while in office, the cot it just a fact of life. She has recently returned to full-time work after having her second baby, Edward, in April.

"I've always been pretty efficient with my time, with children it takes it to a new dimension," says Ms O'Dwyer, who is also Acting Treasurer while Scott Morrison takes a post-budget break.

At three months old, Edward is understood to be the first baby to attend a cabinet meeting. He attended a couple of meetings via teleconference as a newborn and last week in Canberra was allowed in to the exclusive surrounds of the cabinet suite to meet the senior ministry. Prime Minister Malcolm Turnbull asked for a cuddle.

Greens senator Larissa Waters made headlines last month as the first woman to breastfeed on the floor of Parliament, even moving a motion on black lung disease while feeding. Away from the cameras, Ms O'Dwyer has recently become the first woman to breastfeed in a cabinet meeting.

"Where he did need to be fed, as babies do, I was able to do that," Ms O'Dwyer says. "I had the benefit of a mute button down the other end."

Ms O'Dwyer officially took several months of maternity leave, staying at home in Melbourne to look after Edward. But – at her behest – continued to attend cabinet and some other meetings, and stayed in regular contact with Mr Morrison and Finance Minister Mathias Cormann.

Asked if the demands of being a cabinet minister make it impossible to take a large chunk of maternity leave, Ms O'Dwyer says "everyone has a different approach to it".

"Edward is my second baby, so I knew a little bit more what to expect and I think that allows you the ability to plan around that."

Ms O'Dwyer also has the full-time support of her husband Jon Mant. Mr Mant has taken leave from his finance job for six months to care for Edward, just as he did with their first child, Olivia, who is two.

Ms O'Dwyer lists several priorities for the rest of the year. This includes closing loopholes for large multinational companies and "making sure superannuation works for individuals". Last month, the government launched a Productivity Commission review into the efficiency of the $2 trillion super system. On Friday, Ms O'Dwyer announced a bill to make sure employers don't use individuals' salary sacrifice contributions to hold back the amount of super they pay workers.

She is also waiting for a review on the black economy, due in October. As part of this, it has been floated that large denominations, such as $100 notes may be phased out. Ms O'Dwyer said the government is not looking at changing any denominations, but adds it is "interesting" that some countries have placed limits on certain items that can be purchased in cash.

The start of Ms O'Dwyer's maternity leave in April was overshadowed by reports she was facing a push to unseat her in her blue ribbon Melbourne seat of Higgins. Tony Abbott's former chief-of-staff, Peta Credlin, was floated as a possible challenger, although Ms Credlin said she was not interested.

When asked about the push, which was reported barely a week after Edward was born, Ms O'Dwyer does not want to elaborate. "I choose not to dwell on it, I look forward."

Earlier this week, new Liberal Party president Nick Greiner acknowledged the party "has a problem with women and clearly have not done as well as our political opponents in terms of gender diversity". With women making up just 21 per cent of its federal ranks, Ms O'Dwyer says there is no "silver bullet" to address the issue, but adds women need to be selected for winnable seats.

"We need to be very upfront about the fact that we need to be preselecting women for not just marginal seats, but what we consider to be slightly stronger seats," she said, noting there is "no such thing as a safe seat".

Having role models in parliament is also vitally important.

"Particularly women of different backgrounds and different experiences. I think that people need to see there is a career for them, and they can continue to be a mother or choose to be a mother."