Nicky Hilton Says Sister Paris 'Is on Cloud Nine' as First-Time Mom to Son Phoenix Barron

CJ Rivera/Getty Images Paris Hilton and Nicky Hilton Rothschild

Paris Hilton has taken to motherhood like a pro.

At Friday's 16th Women in Film Oscars Party in Los Angeles, her sister Nicky Hilton Rothschild told PEOPLE that the Paris in Love star is "great" as a first-time mom to her and husband Carter Reum's 2-month-old son, Phoenix Barron.

"She is on cloud nine. She is such an incredible mother," added Nicky, 39. "She was born to do this, and I'm just so happy for her."

RELATED: Paris Hilton Says She and Carter Reum Have 20 Boy Embryos Frozen and Are Still Trying for a Girl

She noted that her daughters Lily-Grace Victoria, 6, and 5-year-old Teddy Marilyn — whom she shares with husband James Rothschild — have yet to meet their newborn cousin as Paris and Nicky's respective families live on opposite coasts.

"I'm just so excited for all the cousins and babies to be together. They haven't all met yet," she explained. "When my kids have spring break in a few weeks, they're going to come here and meet their new cousin."

Jeff Kravitz/FilmMagic

Nicky added that their mother Kathy Hilton also "just so, so happy" to be a grandmother again.

RELATED: All About Paris Hilton's Baby Boy Phoenix Barron

Paris told PEOPLE that she and Reum, 42, welcomed their first child via surrogate in January.

"It's always been my dream to be a mother, and I'm so happy that Carter and I found each other," she said at the time. "We are so excited to start our family together and our hearts are exploding with love for our baby boy."

The Simple Life alum also made the announcement on Instagram with a photo of Phoenix's tiny fingers gripping her thumb. "You are already loved beyond words 💙," she wrote in the caption.

Nicky was one of many to celebrate her sister's big news, posting a sweet tribute with a throwback photo of the two of them as children with their own mom.

RELATED VIDEO: Paris Hilton Says Fear of Childbirth from Past Trauma Led Her to Use a Surrogate: 'I'm So Scared'

"Welcome to mommyhood @ParisHilton! 👶🍼🧸 So so incredibly happy for youuu! 🥰 It's the most beautiful ride. There is no greater love," wrote Nicky in the caption. "You are going to be the best mommy. What a lucky boy! 💙"

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Paris previously told Glamour UK that she and Reum have frozen 20 embryos, "all boys," noting that they're trying for a girl. "I just went through the process again a month ago, so I'm waiting for the results to see if there's any girls," she said last month.