According to a source, Kylie Jenner's 6-week-old daughter Stormi's closet includes "everything from designer clothes to tons of shoes"

By Jen Juneau and Aili Nahas
March 19, 2018 01:55 PM

Kylie Jenner is enjoying all the perks of being a mom to a baby girl.

A source tells PEOPLE that the Lip Kit mogul “is having so much fun with” daughter Stormi, 6 weeks, adding, “She’s a great mom and she loves dressing Stormi up in outfits!”

“She’s a little doll. And she has the most incredible wardrobe — everything from designer clothes to tons of shoes,” the insider adds of Jenner’s newborn. “And everyone is really proud of how Kylie is doing.”

The source also tells PEOPLE Jenner’s relationship with boyfriend Travis Scott is going well, but that he’s very busy and there has still been no talk about an engagement.

Want all the latest pregnancy and birth announcements, plus celebrity mom blogs? Click here to get those and more in the PEOPLE Babies newsletter.

Kylie Jenner and daughter Stormi
Kylie Jenner/Instagram

Last week, a source divulged to PEOPLE that Jenner, 20, “is very protective of Stormi.”

“Kylie is socializing with her friends as well and includes Stormi. Of course, she doesn’t want her baby to get sick while she is little,” the insider explained. “It just seems normal and she is definitely not hysterical about it. It is, after all, still the flu season.”

Kylie Jenner’s daughter Stormi

Little Stormi is already developing her own social circle, too. She and cousin ChicagoKanye and Kim Kardashian West‘s newest addition, born Jan. 15 — have enjoyed quite a bit of time together already.

RELATED VIDEO: Kendall Jenner Says the Birth of Sister Kylie’s Daughter Stormi Has ‘Made Us Even Closer’

“Kim and Kylie live very close to each other and spend a lot of time together,” last week’s source told PEOPLE at the time.

“Kylie brings Stormi to Kim’s house. Stormi is around the other kids, including Chicago. It seems too early to call it play dates though.”