Kylie Jenner Treats Stormi Like a 'Little Doll': 'She Has the Most Incredible Wardrobe,' Says Source

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.

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.”