Jessica Simpson Recovering Well From Welcoming Birdie After Difficult Pregnancy

Jessica Simpson is "savoring every minute" of life after the birth of her newborn daughter Birdie following a difficult pregnancy.

The designer welcomed her youngest child with husband Eric Johnson via C-section on Tuesday, March 19, following an extremely difficult pregnancy, but according to sources close to the "I Think I'm in Love With You" singer, she is recovering well, "feeling good," and enjoying life as a mom-of-three.

"She had the best attitude about her recovery," a source told PEOPLE. "She was very excited about having another baby girl. Her older kids were around [the hospital] a lot and doted on the baby."

"The baby is doing really well," a second source added. "Birdie is perfect, and Jessica is savoring every minute. Her family has been back to visit at the hospital and they are elated. They are just soaking it all in."

The singer-turned-lifestyle-entrepreneur had been open about her difficult pregnancy in the month's leading up to Birdie's birth, revealing that her pregnancy journey had been riddled with extremely swollen feet, struggles with sciatica pain, and a battle with bronchitis that even landed her in the hospital.

In the days that followed Birdie's birth, Simpson was sure to give herself a little TLC as she allowed her body to recover, the singer reportedly staying in a $4,000 per night luxury birthing suite at Cedars-Sinai Hospital in Los Angeles.

The suite boasts a personal doula available at all times, a meal delivery plan, two luxury bathrooms with a full-size tub, a lounge area, and multiple beds for visitors. While baby is snoozing, Simpson and her visitors can watch TV on a flat-screen television and browse the web on the hospital's Wi-Fi.

Simpson's visitors have included her father, Joe Simpson, as well as her sister, Ashlee Simpson, who admitted that she now has "[baby] fever a little bit" after meeting Birdie. Simpson's other two children have also visited.

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While Simpsons two eldest children, 6-year-old daughter Maxwell "Maxi" Drew and 5-year-old son Ace Knute, are "so in love with her little sister" and "can't get enough of the baby," there is already a little sibling competition. The source revealed that Maxwell was slightly disappointed that she was bumped out of holding the title as largest baby, as she had been "hoping to maintain her record of the biggest baby in the family" with her 9 pound, 13 ounces birthweight, which was topped by Birdie's nearly 11 pound birthweight.

Simpson is now said to be "very focused on her family and making it fun for the kids" as they adjust to being a family-of-five.