July 06, 2016 11:30 AM

A text from Kim Kardashian West was the invite that landed Chrissy Teigen‘s new daughter Luna Simone her first role in Fergie‘s sexy “M.I.L.F.$.” music video.

“Kim texted me, ‘Hey, Fergie is shooting a video,’ and [she] said, ‘You should be in it,’ ” the new mom told PEOPLE Monday at a Fourth of July barbecue she was hosting at the Revolve summer house in Southampton, New York.

The 30-year-old model’s answer, just weeks after giving birth?

” ‘Absolutely, Kim, what days are you shooting? I’m in,’ ” Teigen says. “It was so much fun to do. I love Fergie. I love her music. And it was just really nice.”

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“Obviously, Luna is in it. But they closed down the set [because] Luna was so new,” Teigen explains. “She was maybe 4 weeks old. They turned off the air. They cleared people out. And it was her natural lunch time anyway.”

The moment of Luna breastfeeding on camera was apparently impromptu, according to Teigen — and husband John Legend, 37, was there too.

“It was [like], ‘[Luna’s] here, and it’s “MILF Money” — I would love to capture this moment with her,’ ” she says. “I think it’s beautiful.

“They were so accommodating of a newborn baby, and John was watching,” Teigen adds. “Honestly, it was like 10 minutes, but it went by so fast. I loved it.”

And did Kardashian West appear as sexy in person on set?

“I was with Kim in a scene, obviously. And what I realized is that I need to live in latex,” Teigen jokes. “Everyone is talking about how we were all Photoshopped. No, you’ve never seen anything like latex. What looks like denim jeans [on Kim], that’s latex.”

RELATED VIDEO: Cutness Overload! Chrissy Teigen And John Legend Share Adorable Snaps of Their Baby Luna

She continues, “And latex gives where it needs to give and cinches when it needs to cinch. In the bouncing scene, Kim was wearing a latex robe, latex high-waisted pants. And when I was wearing the gold — all latex. Honestly, I wasn’t feeling my sexiest, but when you get on that set and have everyone rooting for you, and have this song going, that makes you feel sexy.”

While she looked sensational in person at the Revolve barbecue, Teigen shares that she doesn’t feel 100 percent back in shape since welcoming her baby girl.

“No, I’m not back yet by any means,” she says. “I think people think that I’ve snapped back, but I really have just, in fact, been utilizing undergarments more. I never was a Spanx person or a waist-trainer person. Now I do it. It looks great on the outside, but trust me, I’m a bit soft.”

As some time has passed since the shooting of the video and Luna is now almost 3 months old, PEOPLE also asked about her latest passion.

“Her daddy,” answers Teigen. “Luna is into her daddy more than anything.”

While she’s too young to say ‘Daddy,’ according to Mom, Luna does have a new way to communicate.

“Just this week, she started giggling,” adds Teigen. “It’s unbelievable — it warms your heart so much to see her giggle. In the morning, she wakes up with the biggest toothless smile.”

The proud mom and wife continues, “She looks up at John and is so thrilled to see him, and then she’ll also giggle when you do the raspberries. She loves a raspberry. I do it on her tummy.”

Jeffrey Slonim

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