It's fake. First, that eagle is huge and it's claws are ridiculously sharp. It would certainly injure the baby. Also if you watch closely the baby continues to levitate after the eagle lets go. It's done by animation students.
Those fuckers are huge. in 6th grade I was in a birds of prey club where we got to help care for eagles and take home baby barn owls, but i got to hold a Golden Eagle at a Camp in Sonora and that fucker was just about as big as me.
"Stop what you're doing, cuz I'm about to ruin, the image and the sound you're used to. Look here, I love that Humpty song. Stop cramping my style, man." SI