Christie Brinkley's Daughter Sailor Reveals She Didn't Want to Join 'Dancing with the Stars' at First

Sailor Brinkley-Cook may be in the running for the daughter of the year but stepping into her mom’s dancing shoes certainly was not easy.

After Monday’s premiere of Dancing with the Stars, the Sports Illustrated model, 21, opened up filling in for her mom, Christie Brinkley, who fell and broke her arm during rehearsals on Thursday.

“I didn’t want to at first, honestly,” Sailor tells PEOPLE. “I was terrified. It was a very scary thing for me. The whole idea of having to be live on stage, be on TV dancing, that’s something I’ve never done before.”

“I was so scared, but that was the reason I had to do it,” she continues. “I had to surpass the fear. I had to be stronger than the things that scare me.”

“[My mom] told me to have fun with it and to not let fear stop me from doing any of it,” Sailor adds.

During the premiere, Sailor donned a white, floor-length gown, which was the same one designed for Christie, 65, as she danced the foxtrot to Billy Joel‘s “Uptown Girl.”

“Sailor is truly one fearless, strong, amazing person who just always impresses me,” Christie told PEOPLE before the premiere.

And her pro partner Val Chmerkovskiy shared the same sentiment.

“Obviously it was a very extraordinary situation, but it wouldn’t be Dancing with the Stars without a little excitement,” Chmerkovskiy, 33, told PEOPLE. “In fifteen seasons I’ve never had an experience like this.”

Still, he said, “I’m glad I did. I’m glad I was the one that was put in this position. I’m really grateful for the challenge and I’m grateful I got to share it with an awesome person like Sailor.”

Christie’s nasty fall left her with multiple broken bones, which required surgery to insert a plate and screws to repair her shattered arm. The supermodel also dislocated her wrist and, on top of that, had already twisted her ankle earlier in practice.

After undergoing surgery on Friday, the star — who previously survived a horrific helicopter crash, as well as a serious horse and car accident — remains on heavy pain killers.

Aside from the physical injury, Christie is also dealing with the emotional fallout of not being able to compete.

“I’m telling you I was having the time of my life,” she told PEOPLE.

“So it was really, really a crushing, crushing disappointment in every way. Literally, figuratively everything that happened. And one of the worst feelings is to feel like you’re letting anybody down, you know?”

Enter Sailor!

“I’m doing this mostly for my mom!” Sailor said during the premiere. “I just want to make her happy and make her proud.”

“She loved doing this, she loves dancing and she loves performing and getting hurt was her worst nightmare,” she added.

Dancing with the Stars airs Mondays at 8 p.m. ET on ABC.