The Derry man will lead his country for the first time in a must win game for Ireland, who need victory to secure qualification for next summer's tournament.
"Our players have respect for Ireland", he said at a pre-match press conference in Lansdowne Road.
He said: "He's captain material".
"My head, however, says something different and I'm anxious".
Duffy said: "I just think I'll sort of be myself".
McCarthy, speaking on the eve of the game, said that Duffy "has been important for the team for a long time now. But the main goal is to go out and play and try to get the victory".
In a one off game though, and playing at home, the Boys in Green will feel that they can, as they have done in the past, pull out a big result when the chips are down.
Swiss permutations Ireland will have an extra element on their minds against the Danes: they will need a 2-0 win to qualify if Switzerland only manages to take four points from its upcoming meetings against Gibraltar and Georgia - even though that's unlikely.
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"Without going around screaming and shouting and cajoling people, he gets people up".
"I am excited about it, my family will be proud and I will be too".
"If you are having a tough time, he rallies the troops and gets them defending. He's one of those guys that you rely upon".
More recently, Denmark hammered Ireland 5-1 at the 3Arena in the second leg of their World Cup qualifying play-off back in 2017.
Few pundits gave the Irish much hope of a top-two finish so it's to McCarthy's enormous credit that they head into the final qualifier with a chance of jumping above the Danes.
Ireland manager Mick McCarthy intends to give younger, inexperienced talent an opportunity to impress against the All Whites, but he will make sure the "Big Guns" are primed and ready for the Red and Whites on Monday.
They have also gone 33 games unbeaten in 90 minutes under Åge Hareide.
"My heart says that, having overachieved so far, we can have one more incredible night at the Aviva and Mick can see the rewards of his efforts and get us over the line with a win over Denmark". "Get a good start, get after them and have a good night". "They surely won't want to reduce to us, that's for sure".