Cooper was controversially benched for the Wallabies' opening loss to New Zealand in the Rugby Championship, with new coach Ewen McKenzie handing Matt Toomua the number 10 shirt at Sydney's Olympic Stadium.
Although Toomua had a solid test debut in the stinging 47-29 defeat, some Australian pundits have called on McKenzie to re-install the mercurial Cooper at flyhalf for Saturday's return match in Wellington.
Regardless of where he starts, Cooper can expect another frosty reception from All Blacks fans, who have never forgiven the Tokoroa-born 25-year-old for alleged 'cheap shots' on skipper Richie McCaw in previous matches.
"I think it's something Quade's dealt with quite well because I think it's quite unreasonable what the All Blacks supporters are doing to him," flanker Hooper told reporters in Melbourne on Monday.
"He's a great player and a really good guy. I think everyone who enjoys footy wants to see him do well and I think the boo-ing is a bit below the belt sort of stuff.
"He deserves more than that as a player and I think he's got more to bring. With time on the field and the sort of performances he can put on there, that'll change and the boo-ing will go because people want to see him play.
"(A reception) like that would spur you on to prove them wrong, so I think he's got it under control."
Having never played his best rugby against New Zealand, Cooper came on for the last 18 minutes in Sydney and struggled to make an impression with the game already out of reach.
He was not alone, however, with a number of his backline team mates failing to breach the All Blacks line while also making costly defensive errors.
The loss will ensure Australia slump to fourth in the world when new rankings come out later on Monday, with England leapfrogging them into third.
Defeat in Wellington would see the Wallabies surrender the Bledisloe Cup, the symbol of trans-Tasman Sea supremacy, for an 11th straight year.
Hooper, his team's best in Sydney, agreed the world champions had a psychological hold over Australia.
"They've held the (Bledisloe) Cup for the last 10 years so there's definitely a bit of that," Hooper said of the mental edge.
"But in saying that they'd be nervous about losing it and we really want it.
"Obviously it was the first game for a few people and a few things like that, and (with) new combinations you're going to have those sort of teething errors ... I think that despite that, the boys did pretty well."
A menace at the breakdown and a strong runner with the ball, openside Hooper won Australia's player of the year in the Super Rugby competition with the New South Wales Waratah.
A contract extension announced on Monday, which will keep the 21-year-old tethered to Australia until 2016, is a welcome boost for their preparations for the 2015 World Cup.
A pair of black eyes underlined the hard work Hooper put in on Saturday night, when he locked horns with New Zealand's inspirational captain Richie McCaw.
Despite coming back off a long sabbatical, McCaw scored a try in a typically combative display that left Hooper singing his praises and relishing his next chance to face the 32-year-old.
"He didn't skip a beat, did he? He was on-song, menacing as ever," Hooper said.
"It was a great challenge for me, seven against seven. That's something really enjoyable about test footy is that you get to play these guys.
"Six months and he didn't go missing at all."