Drew Barrymore, Will Kopelman and dog Douglas
12/20/2012 at 12:25 PM EST
She may have been a nervous wreck
after baby Olive arrived this fall,
but the Drew Barrymore
could have rested easy because her dogs had everything under control.
"They're so protective of her. They're so sweet," she tells PEOPE of her pups, Douglas and shepherd mix Oliver
. "And Douglas, the little blonde one, just comes and licks [Olive's] head, and it's just so goofy and silly and I always say, 'Douglas, is this your baby?' "
The first-time mom, 37, and her husband Will Kopelman
were careful when it came to introducing their furbabies to the real baby.
"We brought her stuff home to them to sniff and play with," she tells PEOPLE. "I put her with them right away. I was holding her and protective but there are all these wonderful studies that kids that grow up with dogs have better immunities because of the dander and the pollen. And it's a proven fact that dogs just improve the quality of your life."
In just a few months, Douglas has assumed the role of bodyguard over 10-week-old Olive, whom Barrymore calls "Super Baby" because she sleeps and eats so well.
"He's literally sitting [and] looking out the window," she says, "in, like, a guard dog position."