The Danes and Socceroos are in Group C along with France and Peru and will meet in Samara on June 22 (AEST).
Kjaer, who plays his club football for Spain's Sevilla and will face Bayern Munich in the UEFA Champions League quarter-finals next week, said Bert van Marwijk's men are more seasoned campaigners in international tournaments.
"Some people in Denmark have claimed that this is not a difficult group for us - maybe rather the opposite - but I do not agree," Kjaer, 29, said.
"Australia are a strong team with valuable experience from major tournaments such as the World Cup, Asian Cup and Confederations Cup.
"This is something we lack in Denmark after having not qualified for the last six years for the World Cup or the Euros.
"Australia are Asian champions and that says a lot about their quality. Their latest results could confuse a bit but they don't really confuse me because in trial matches you never really know.
"A draw with Colombia is a top-class result whereas losing to Norway is obviously less impressive."
Denmark and Australia qualified for the World Cup finals via a playoff.
The Danes overcame Ireland 5-1 in Dublin after a home 0-0 draw thanks largely to a hat-trick from Tottenham Hotspur hot shot Christian Eriksen while the Socceroos had a treble from Aston Villa's Mile Jedinak to thank for a 3-0 win over Honduras after a 0-0 draw in San Pedro Sula.
Kjaer, who plays in the centre of defence, said there is little difference between the two teams even though Denmark (12) are ranked much higher than Australia (37).
He acknowledges that the flamboyant French are the team to beat in the group.
"When you look at the world rankings we are three teams in the top 12 right now and that shows real high quality," he said.
"But the FIFA rankings do not give the full picture ... they also tell us that France, Peru and ourselves win a lot of matches which is why we occupy such high positions.
"Obviously France look like the favourites to win our group. If the French live up to their potential, they are definitely among the top contenders for the world championship ... and you cannot really say that about the rest of us.
"I believe that we look very even in level but let's see. It's a very competitive group and we are looking forward to that challenge. It is our clear goal to advance from the group stage but I am pretty sure that we share that goal with Australia and Peru."
Kjaer admitted he does not know much about the Australian team but he knows that the Socceroos do not have a reputation as great competitors for nothing.
"They are a hard working, well organised and honest football team," he said.
"As I said, Australia have a lot of World Cup experience since this is their fourth straight finals appearance. They also have experience from other tournaments like the Asian Cup and Confederations Cup and they will surely benefit from that in Russia.
"I know Maty Ryan privately. We have met because we have the same agent and he is a great guy. As a football player I know him to be super professional and a great goalie, which he proves now in Premier League."
Kjaer, who missed the first part of the year due to a calf injury, is back in full swing and he played a key role in Sevilla's defeat of Manchester United in the UCL's round of 16.
He was back in the Danish team that played two internationals in the most recent FIFA break.
They beat Panama 1-0 in Brondby and drew 0-0 with Chile in Aalborg.
So what are Denmark's strengths?
"As Denmark captain I am happy to say that the team spirit is our greatest strength," he said.
"We laugh together but we also bleed together and we will work hard to do anything to help each other. Every single member of this group of players knows and appreciates that we are nothing without each other.
"That is not necessarily the truth about all teams in football. But we share that feeling and ability and that makes the unit stronger than just 11 individuals in the same jerseys.
"I enjoyed having Morten Olsen as national coach but then he left us two years ago and Aage Hareide took over with a new style and new ideas. It has changed our way of playing - we got more flexibility in our systems, we can change our game plan and that made us more difficult to read."