The Hoops appointed the 65-year-old following the dismissal of Mark Hughes, who left the team winless after 12 matches. A defeat to Manchester United and two draws followed to leave the team seven points away from escaping the relegation zone.
Redknapp has previously led West Ham and Portsmouth to safety following relegation battles, and took over at Tottenham when the North London side were bottom of the table, before eventually taking them to a Champions League quarterfinal.
But when asked if leading QPR to survival would be his finest feat as a manager so far, he told reporters: "Of course, absolutely from where we are.
"We will try. It is going to be hard. I've taken a big task on here. I know what I've taken on, I'm not a fool. It's going to be difficult but you can only give it your best."
Chairman Tony Fernandes has invested heavily in the squad in each of the past three transfer windows but the club avoided relegation only on the last day of last season following five straight home victories, but this term the Hoops are still winless after fifteen matches.
"It always creates anxiety when you're bottom of the league and can't get a win," Redknapp continued. "Football is like life - it is about confidence. When things are going well, you win games and you don't know how you won. You come off thinking 'we were rubbish today but we won again'.
"Sometimes, like we are at the moment, you play well but you can't get the win and that's how it goes. They have shown a good attitude. They've trained hard, worked hard. They've all been good, they're good lads. We just need a win, don't we?
"We could have got that win on Saturday with a bit of luck. We would be back in there, chasing the pack, but we couldn't quite get those three points."
Redknapp restored Shaun Wright-Phillips to the lineup for his first start in six matches in Saturday’s 1-1 draw against Aston Villa, and praised the midfielder for his display.
"I think confidence is the key for him. He has to play with confidence," he added. "He made some good runs and great ones in the first half, where he should have scored and then hit the post.
"But he bent his runs in off the line and looked lively. He has done well in training and I gave him a chance."