Eminem’s Daughter Hailie Jade Is ‘Soaking Up Every Moment’ of Being a Mom Ahead of First Christmas with Son Elliot Marshall (Exclusive Source)

Hailie Jade McClintock is enjoying all the highs of motherhood.

Eminem‘s daughter, 29, and her husband Evan McClintock welcomed their son Elliot Marshall on March 14. Months later, a source tells PEOPLE that the couple’s first baby continues to bring them joy as he marks new milestones.

“Elliot just hit that really exciting stage where he’s curious about everything. He’s reaching for things and trying to move around on his own,” the source says. “It’s adorable to watch him explore, and Hailie is soaking up every moment.”

The insider adds that the influencer “still can’t believe she’s a mom” at times. “It almost seems too good to be true,” the source continues. “She and Evan are so looking forward to celebrating their first holiday season as a family. They couldn’t be happier.”

PEOPLE has reached out to representatives for Hailie Jade for comment.

Hailie Jade announced her son’s arrival in April when she shared a photo of Elliot on Instagram. A sign with his full name and birthdate revealed that the influencer named her child after her Grammy-winning father, whose real name is Marshall Mathers.

In June, Hailie Jade — whose mother is Eminem’s ex-wife, Kim Scott — opened up to PEOPLE about the challenges of raising Elliot in the public eye, just as she was brought up by Eminem when she was young.

“Having been in the spotlight for so long, I’ve learned the importance of balancing what I share publicly with what I keep private,” she shared. “Over time, I’ve come to understand the struggle my father faced — wanting to protect our privacy while also feeling proud and wanting to celebrate his kids.”

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The Just a Little Reno YouTube creator explained how she can relate to her dad in new ways now that she’s experiencing parenthood for herself.

“I want to share the proud, joyful moments that mean a lot to me, especially as a parent, but I’m also intentional about keeping certain parts of our lives just for us,” she told PEOPLE.