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"I'm so happy, I can't bear it," the actress says. "I'm so in love with her."
Daughter Frances Pen was born Feb. 20 to 35-year-old Peet and her husband, screenwriter David Benioff, 37.
But Peet admits that the early days were difficult. "In the beginning it's hard ...because they aren't giving you anything back and you think you're supposed to be really happy, but, in fact, you're actually psychotic because of sleep deprivation," she says.
"But now it's beautiful. It's like I'm in love with someone else," Peet told PEOPLE at Glamour magazine's Fashion Gives Back Party in New York City.
With her daughter getting increasingly active, the TV and film star has been forced worked out a daily routine. "We wake up and play, she naps and I do my own thing like check e-mail, we have lunch, then she naps again," she says, adding, "She's obsessed with avocados!"
"I mash them up and feed them to her," says Peet. "I mash everything up like peaches, mango, peas and carrots."
Meanwhile, there will be more denim than frills for Frances if she grows up liker her daddy-approved nickname: Frankie.
"My husband loved the name, and, when I was younger, I loved the book The Member of the Wedding," Peet explains. "That character was kind of sad, but she's a super cool tomboy."
• Reporting by SUSAN YARA
