updated 06/27/2012 AT 6:00 AM ET
•originally published 06/26/2012 AT 6:50 PM ET
The new mom, 31, took to cyberspace Tuesday with a new look at her daughter with fiancé Eric Johnson.
“Howdy friends,” the Fashion Star judge wrote, accompanying a photo of her pouty-faced little one, clad in red and white stripes.
About a week after the May 1 birth of Simpson’s pride and joy, she Tweeted, “I am so in love with baby Maxwell. I want to cry every time I look at her. Motherhood is by far the best thing I’ve ever experienced.”
Since welcoming her new addition, “life has completely changed,” Simpson told PEOPLE last month. “From how I sleep to what I think about, Maxwell has definitely taken over everything!”