Cullip is expected to make his debut against Burnley this weekend following his move from Nottingham Forest.
And he told The Gazette: "Without a shadow of a doubt I believe we can stay up.
"From what I've heard we've been creating chances and been unlucky to lose games. We've just got to keep battling away and I'm up for it.
"It's a good move for me and I'm looking forward to playing for QPR. I'm a determined and vocal player and anyone who knows me knows I'll give total commitment."
Bolder made his debut in the midweek defeat at Barnsley which left Rangers in the bottom three.
But the midfielder is also confident that his new club will avoid the drop.
"I've been in this position before with Derby," Bolder said.
"It's a dogfight and I for one believe we'll come out of it a Championship club.
"I wouldn't have come here if I thought I was going to be playing in League One next season.
"We dug in and battled and had the chances to beat Barnsley. The lads have told me that's been the story of their season and happened against Luton in the FA Cup.
"We're creating chances, but all that's important at this stage is results and I'm confident we can get them."
He added: "Derby are like QPR in that they've been in the top division, had some good times and then struggled.
"They're at the top now and that kind of turnaround can happen and happen very quickly – Watford did it as well.
"What has to happen though is that we stick in this division. We must not go down. Stay up, and with a bit of strengthening we can push on from there."