Jessica Simpson's Baby Maxwell Is "Eating Like a Champ"

Maxwell Drew Johnson has a maximum appetite!

Just one day old, Jessica Simpson's baby daughter (who weighed 9 lbs. 13 oz. at birth) is "eating like a champ and has a big appetite" while staying with mom at the hospital, a source tells Us Weekly.

"The birth went smoothly," adds the source of Maxwell, born Tuesday morning at Cedars-Sinai Medical Center in Los Angeles.

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The singer/designer, 31, and fiance Eric Johnson "are over the moon about the baby," the insider says.

Although she's set to remain at the hospital for "the next few days" to recover, Simpson "is already up and walking around," the source adds -- and bonding with her little girl.

"Everyone is marveling at what a natural Jessica is," the source tells Us. "She was born to be a mom!"

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As previously reported, Simpson's family -- parents Joe and Tina, sister Ashlee -- and Johnson's parents were in the hospital for the baby's birth. "That's how Jessica and Eric wanted it," explains the insider

One rumor that's apparently unfounded: TMZ's claim that Simpson et al are ensconced in a super-luxe birthing suite costing nearly $3,800 a night (more than the $3,200-a-night NYC suite used by Beyonce and Blue Ivy Carter n January).

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"She does have a suite at Cedars, but it is definitely not in the $4,000 a night price range," the insider says.

Gushed Simpson and former NFL pro Johnson, 32, in their Tuesday birth announcement: "We are so grateful for all of the love, support and prayers we have received. This has been the greatest experience of our lives!"

This article originally appeared on Usmagazine.com: Jessica Simpson's Baby Maxwell Is "Eating Like a Champ"