Fly-half Cooper will be pivotal to Australia's hopes of knocking out holders South Africa in their World Cup quarter-final clash on Sunday.
World Cup winners following their triumph at England's expense in Paris four years ago.
But Cooper and company, having already beaten the Springboks twice this year, also hold designs on meeting New Zealand or Argentina in next Sunday's second semi-final.
"I guess, like everyone, I am still in awe of some of the things he (Cooper) does," McCabe said.
"I think his unpredictable nature is one of his best strengths.
"I am still not 100% sure what he is going to do next, but I am starting to feel really confident with him."
McCabe's return from a shoulder problem - plus the reappearance after injuries of players like David Pocock and Digby Ioane - will strengthen Australia's bid to stun the Springboks.
"I've sort of ticked all the boxes this week in terms of building up contact and that sort of thing, so I am 100% confident in it this week," McCabe added.
"There were obviously some pretty dark moments in the dressing room after the game (against the United States). I thought I was gone for the tournament and wouldn't be able to experience what is coming tomorrow."
Australia have reached the last eight despite suffering a pool stage defeat against Ireland, and McCabe said: "Obviously, with a lot of the guys I was disappointed in how I played against Ireland.
"Those initial ball-carries that I didn't get to ground, that cost us a lot in the first-half. I am looking forward to hopefully making amends and having a good performance on the weekend."
South Africa will once again be without injured lock Bakkies Botha, but Springboks assistant coach Gary Gold has hailed the quality of Danie Rossouw, who will partner Victor Matfield in the second row.
"The history of World Cups has shown that teams that have been able to have guys who are reasonably versatile in those types of crucial positions is important," Gold said.
"Danie is absolutely essential for us. He played in the back row during the Tri-Nations for us, and he got some pretty good game-time doing that.
"The players are quite calm at the moment. The training sessions have gone well this week and the enormity of the situation is certainly something we are aware of.
"Ever since we went into camp in Johannesburg we spoke about the responsibility that all of us have got to everyone back home.
"We know the strength of the support back home and it is something that is very important to us."
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