Australia were in danger of a humiliating early exit after a surprise defeat to Nigeria but they are now into the Women's World Cup quarter-finals and belief is growing that they can go all the way.

Throw a returning Sam Kerr into the mix and add in the departure of holders the United States, and the co-hosts sense that a first World Cup triumph is within their grasp.

The 3-2 loss to Nigeria in the group phase put Australia's hopes in peril but they responded with a 4-0 thumping of Olympic champions Canada and beat Denmark 2-0 in the last 16.

Skipper Kerr's belated appearance at the tournament after a calf injury made the headlines but it was Caitlin Foord and Mary Fowler who together blew Denmark away in front of nearly 76,000 spectators in Sydney on Monday.

The Matildas will face France or World Cup debutants Morocco in the last eight and they have all the momentum as they close on a first World Cup semi-final and possibly more.

"If we play like this we can beat anyone," Arsenal forward Foord said after giving the Danes a torrid time with her pace, movement and power.

The 20-year-old Manchester City forward Fowler was just as impressive.

It was her vision and inch-perfect ball down the left wing which teed up Foord for a clinical finish in the first half at a near-capacity Stadium Australia.

Fowler was instrumental again in the second goal, 20 minutes from time, with Hayley Raso applying a deadly finish.

But one of the biggest cheers was yet to come, when 10 minutes later talismanic striker Kerr climbed off the bench for her first action at the tournament.

There was a nervous moment for the home fans when she slipped late on, but the Chelsea goalscorer appeared unharmed and her return is perfect timing for Australia.

The 29-year-old still may not start in Saturday's quarter-final in Brisbane, given she is only fresh off three weeks out with her calf problem.

But if Australia are chasing the game she will be the ultimate super-sub.

Foord called Kerr's return "a massive boost for us".

"For (other) teams looking ahead it's pretty scary to know that she's back in the team and she's going to be a part of it with us," she added.

Handling the pressure

And then there is the home support.

A more clinical side than Denmark, who were contesting their first knockout game at the World Cup since 1995, might have punished the home team in the first 20 minutes.

The Stadium Australia crowd sensed their players needed a lift and responded with chants of "Aussie, Aussie, Aussie".

Denmark failed to capitalise on their early dominance and then Fowler and Foord combined to deadly effect to put Australia on their way to a deserved victory.

Australia's coach Tony Gustavsson had tears in his eyes afterwards when asked about the home support.

"I get emotional, I really do," the Swede said.

"The support we feel, thank you. Wow."

Player of the match Foord called the fans their "12th man" and said she felt support for the team building around Australia.

"The whole country is behind us and we do feel it, we do see it," said the 28-year-old.

With growing expectation comes growing pressure, but Foord is confident they can handle it.

"I think you feel pressure when you're not prepared," she said.

"And we feel prepared. We feel like we're ready for any scenario, every match.

"I don't think we feel any pressure, we are just enjoying our performances and building on that," she added.

"We know we have to take it up another level if we want to go all the way."