updated 06/22/2011 AT 12:30 PM ET
•originally published 06/22/2011 AT 8:30 AM ET
Like mother, like daughter.
When Pink and Carey Hart’s week-old daughter Willow Sage posed for her first family photo shoot on June 9, she didn’t miss a beat.
“Willow is a pro!” Pink, 31, tells PEOPLE. “Or else she is borderline narcoleptic like her daddy – she slept the whole time.”
All kidding aside, the Grammy-winner and her motocross-champ husband of five years, 35, are relishing their new roles as parents following Willow’s birth on June 2.