Earlier Friday, she was taken off her respirator and was breathing on her own.
Dozier remains in critical but stable condition at Landstuhl Regional Medical Center in Germany, where she is resting comfortably.
"She is talking well, hasn't lost her sense of humor, and was disappointed that we had to meet in Landstuhl, Germany, instead of over a drink in New York City," CBS News President Sean McManus said in a message to CBS employees.
"She's sharp as a tack. Really," Dozier's father, Benjamin, told CBS News correspondent Sheila MacVicar on Thursday. "She knows where she is. She knows the questions to ask."
Her first question Thursday was: "What (happened to the) crew?" Her family and doctors agreed, if she asked, that she should be told what happened — that James Brolan and Paul Douglas died in the attack.
The coffins with the bodies of were flown on Thursday from Kuwait to London's Heathrow Airport, where a ceremony was held with their families and close friends. Their arrival was honored in a simple, moving ceremony; their plain wooden coffins draped in the Union Jack, CBS News correspondent Mark Phillips reports.
When Dozier heard the news, "You could tell it upset her. She kind of closed her eyes," Dozier's mother, Dorothy, told MacVicar. "I know how deeply she feels, and when she can voice her feelings it will be much easier for her."
On Thursday a young American soldier gave his Purple Heart to Dozier's brother, Michael, to give to Dozier. He told Michael that he wanted Kimberly to have it because, he said, she'd suffered as much as any soldier. That Purple Heart is now beside Kimberly's bed, reports MacVicar.
Dozier was seriously wounded Monday by a car bomb in Iraq that killed Douglas and Brolan. Her mother said Dozier is "going to have to have rods in her legs; they were pretty badly injured."
It is expected that Dozier will be stable in the next couple of days and she will be transported to an appropriate medical facility in the United States on Sunday.
"She has to be stable enough to sustain the flight," Shaw said.
The three journalists, who were embedded with the 4th Brigade Combat Team, 4th Infantry Division, were doing a Memorial Day story about what life is like for the troops in Baghdad when an explosives-packed car blew up nearby.
Dozier, Douglas and Brolan had been riding in an armored Humvee. But at the time of the blast in the Karada section of Baghdad, they were outside on the street, accompanying troops who had stopped to inspect a checkpoint manned by the Iraqi Army. They were wearing helmets, flak jackets and protective eyeglasses when the bomb went off.
Douglas, 48, and Brolan, 42, died at the scene of the explosion, which also killed a U.S. soldier and an Iraqi interpreter and wounded six U.S. soldiers. The soldier has been identified as Army Capt. James Funkhouser, 35, who had been in Iraq only a few months, and leaves behind a wife, Jennifer, and two daughters, Caitlyn and Allison.
Dozier, 39, was flown to the closest U.S. military hospital, which was about a mile away, where she underwent two operations.
Douglas, who was British, leaves a wife, Linda; two daughters, Kelly, 29, and Joanne, 26; and three grandchildren. Brolan, who was also British, leaves a wife, Geraldine, and two children, Sam, 18, and Agatha, 12.
Douglas had worked for CBS News in many countries since the early 1990s, including Iraq, Afghanistan, Pakistan, Rwanda and Bosnia
Brolan was a freelancer who had worked with CBS News in Baghdad and Afghanistan during the past year. He was part of the CBS News team that had received a 2006 Overseas Press Club Award for its reporting on the Pakistan earthquake.
Dozier has been a CBS News correspondent reporting from Iraq for the past three years. Her previous assignments include the post of London bureau chief and chief European correspondent for CBS Radio News from 1996-2002, and chief correspondent for WCBS-TV's Middle East bureau. She has won three American Women in Radio and Television (AWRT) Gracie Awards for her radio reports on Mideast violence, Kosovo and the Afghan war.
Scores of journalists — nearly 75 percent of them Iraqis — have been injured, killed or kidnapped in Iraq since the 2003 U.S.-led invasion that ousted the government of Iraqi president Saddam Hussein.