Three-month-old Noor al-Zahra, who was born with spina bifida, was doing well after the operation Monday at Children's Healthcare of Atlanta.
"She had a peaceful and quiet evening," Dr. Roger Hudgins said Tuesday on CBS News' The Early Show. "The surgery went extremely well."
"She's so delightful. She really does reach out. She looks at you. She's smiling now. She is cooing. She's a real delight to be around," Dr. Hudgins says.
Surgeons on Monday removed a fluid-filled sac from the baby's back and positioned her spinal cord in its proper place, CBS News correspondent Jim Acosta reports.
Hudgins, a pediatric neurosurgeon, said a brain scan would be conducted later Tuesday to determine if there was any buildup of fluid. If there is, doctors might have to operate Wednesday to remove it.
The infant's grandmother and father cried "tears of joy and relief when they learned she was out of surgery and in recovery," said Helen Shepard of Childspring International, the group that provided a host family for them and will arrange medical care when Noor gets back to Iraq.
Christina Porter, the organization's American director, said the grandmother said repeatedly in Arabic: "Thank you, America. Thank you."
Despite the surgeries, Hudgins said Noor likely will be a paraplegic, "typical of a child born this way."
"I think mentally and developmentally, it's my hope that she will be absolutely normal," Dr. Hudgins told Early Show co-anchor Hannah Storm. "She's a very engaging child at this point." He said that she likely would have died without medical treatment from a bladder infection or other problem.
He said the goal is to get the girl well enough so that when she returns to Iraq she will not require a lot of continued care.
Baby Noor wasby U.S. troops raiding a house in Abu Ghraib, a poverty-stricken district near Baghdad. The soldiers noticed paralysis in the baby's legs and what appeared to be a tumor on her back.
In spina bifida, the backbone and spinal cord fail to close before birth. The apparent tumor was actually the fluid-filled sac, which contained part of the baby's spinal cord.
One of the soldiers e-mailed a friend in Georgia who is a social worker. They enlisted the help of a variety of organizations, and Noor, her grandmother and her father were brought to the United States late last month.