Larry Birkhead and Dannielynn
St. Clair/Winslow/Splash News Online
Larry Birkhead says being a dad is "the best experience of my life" – and reveals his pet name for his 10-month-old daughter, Dannielynn.
"I call her 'Little Monkey,' " the proud daddy told PEOPLE at the Hollywood premiere of The Bourne Ultimatum Wednesday. "[It's] because she just rolls around like a little monkey all the time with me. I call her 'Cricket' sometimes too."
Birkhead, who fathered Dannielynn with the late Anna Nicole Smith, said he's been overwhelmed by all the support – and gifts – he's received since winning custody of the baby. "You know I get tons of things from people who I've never even met before and so everything means a lot to me."
He added, "[Dannielynn] loves all kind of toys. She loves anything that makes noises and sounds and lights, and she's really alert – she's just a great baby!"
And the 34-year-old is loving being a father. "It's the best experience of my life," he said. "I get up early in the morning and I run in as soon as I hear the first cries and I take a peek at my daughter and scoop her up. It's great! It's a lot of fun [and] it's a lot of hours."
As for Dannielynn, she's already said her first word – sort of. "It's gaga, said Birkhead, 'but I'm trying to make it Dada."