October 19, 2012 01:00 PM

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Apparently there is too much of a good thing – just ask Jack Osbourne.

The new dad – who welcomed daughter Pearl Clementine with wife Lisa on April 24 – says he’s received an overwhelming overflow of presents for his little one.

Everyone does [spoil her],” Osbourne, 26, tells PEOPLE. “We’ve had to respectfully decline any more gifts.”

But the offerings haven’t been out of the ordinary. “We haven’t gotten anything too crazy,” he says. “There have just been lots of clothes and toys. Not really too outrageous for a baby.”

Aside from having to turn things down, the TV personality says fatherhood is “good,” explaining, “It’s a lot of fun. The best part about it is there’s something new every day. Babies grow so much when they’re this age. They’re constantly changing.”

“You’ll go to bed one night and wake up the next morning and you’ll learn something new. That’s the exciting part,” he shares.

Osbourne, who is also basking in the joys of being a new husband – he married Lisa on Oct. 7 – says everything happening at once can be overwhelming, but, “it passes. It always does. There’s always some relief in that.”

He adds, “It’s all been good, so I can’t really complain.”

Part of what’s helped him manage his new parental status is having Lisa by his side. “Lisa’s the best,” he gushes. “She’s like Supermom 5,000.”

Breaking away from family, Osbourne is New Orleans-bound from Oct. 26-28, where he’s teaming up with Fuse and Scope Mouthwash and to be a news anchor at the Voodoo Music and Arts Experience festival.

“Work is work,” he says of leaving his clan behind. “I’m going to be doing interviews, as well as helping organize some exciting activities we’re doing with the crowd. I’m really, really excited about seeing Metallica. I’m a big Metallica fan. I’ve been to Voodoo fest before and I love the vibe there. It’ll give me the opportunity to check out some new bands.”

Osbourne will also begin his gig as a full-time music news anchor for Fuse in the next few months.

— Dahvi Shira

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