(CNN) -- U.S. Rep. Gabrielle Giffords was successfully transferred Friday to a Houston hospital from Tucson, Arizona, and physicians described the brain-injured congresswoman as "doing great."
"I'm very pleased to bring the news that the transfer of Gabby from the University Medical Center in Tucson to Memorial Hermann Hospital here went flawlessly," Dr. Randall Friese of the UMC Trauma Center said at a Houston news conference.
While saying an assassin's bullet "did damage some portions" of Giffords' brain, Dr. John Holcomb of Memorial Hermann-Texas Medical Center said Giffords is "doing great."
"She could have been a lot worse," Holcomb said. "This was a tangential gunshot wound. Fortunately, it didn't go crosswise" through her brain, he said.
Dr. Dong Kim of Memorial Hermann said a 30-minute exam of Giffords found that she has "very good movement on the left side of her body." He added that her physical therapy and rehabilitation will be a four- to six-month process.
"We tested her vision and she didn't like us shining the light in her eyes and wanted to keep them closed, and these are all very good signs," Kim said.
"She also had pretty good tone in her leg," he said. "She just looked spectacular."
But, he said, "there are varying stages of what we call paralysis or weakness" on her right side.
"In her arm, we are not seeing much tone and we're not seeing much movement," Kim said. But he noted that Giffords did show movement in her arms during her hospitalization in Tucson, so results could change.
"We really think over the next few months she's going to do remarkably well," Kim said. "There's no question that she is aware of what's happening."
Giffords is able to move her lips, Kim said. "Whether she can mouth words, we'll have to wait and see," he added.
Portions of Giffords' skull that were removed are still frozen in a sterile bag, and it could be weeks, if not months, before those portions are surgically returned to her head, doctors said.
"The transfer of that is not a big deal," Kim said of such surgery.
Giffords has been in intensive care for the past 13 days since she was shot in the head January 8 during a meet-and-greet outside a Tucson supermarket. Physicians expressed concern Friday about infection, saying they will be monitoring that over the next few days.
Friese, who accompanied Giffords in the ambulance ride in Tucson from the hospital to the airport, said that Giffords could hear the cheers of well-wishers from the sidewalks Friday.
"She smiled and actually began to tear a little bit," Friese said.
Giffords left the Tucson hospital where she had been treated since alleged assassin Jared Lee Loughner, now in custody, shot her in the head. Loughner, 22, is accused of killing six people, including a judge, and wounding a total of 13, including Giffords.
The congresswoman arrived at Houston Hobby International Airport shortly after 1 p.m. and was flown in a helicopter to Memorial Hermann.
Although previous reports had indicated she would move directly to a rehabilitation facility affiliated with the hospital, she instead was taken to the hospital's trauma center for evaluation and treatment, Kim said.
"She's not quite ready for rehabilitation yet," he said, citing concerns about ongoing medical issues. He declined to elaborate.
The hospital said in a statement that she will be transferred to the rehabilitation facility, TIRR Memorial Hermann, when her health allows.
Giffords left the Tucson hospital in an ambulance escorted by police and a group of motorcyclists from the Veterans of Foreign Wars. The procession traveled to Davis-Monthan Air Force Base, where she was carried aboard an airplane for the flight to Houston.
The move is the latest in a string of milestones for Giffords since the 40-year-old congresswoman was shot in the forehead.
On Thursday, she was able to go outside for the first time since the shooting.
"Today, actually, we were glad to say that we were able to take her outside and she was able to do her physical therapy," Dr. Peter Rhee told CNN's John King.
"We gave her some fresh air and also gave her some sunshine," said Rhee, speaking from outside University Medical Center. "She was able to see the Arizona mountains."
Giffords' husband, Navy Capt. Mark Kelly, described his wife's progress as "remarkable" Thursday, saying he is hopeful she will make a full recovery.
"I've told her that," Kelly told reporters at University Medical Center. "She recognizes it. ... She is a fighter like nobody else that I know."
Giffords is able to stand with assistance, but is not yet able to take steps or walk, said Rhee, adding that therapists are helping Giffords with ways to express her thoughts and, eventually, speak.
"(We are) holding her up so she can train herself to hold her head up," Rhee said. "She is learning to balance and learning all the little things we can take for granted."
On Wednesday, the public learned that Giffords was able to rise from her hospital bed and stand with assistance.
Kelly said he believes she has tried to speak, although she is prevented from doing so by a breathing tube in her neck; and he believes she is aware of her surroundings, saying he can look into her eyes and tell. She will smile at him and pat him on the face -- something she did before the shooting, he said.
"Every time I interact with her, there's something quite inspiring," he said.
A federal grand jury indicted Loughner on Wednesday on three charges of attempted murder. The indictment charges Loughner with attempting to kill Giffords and two of her aides, Ron Barber and Pamela Simon.
Legal experts said that more federal charges against Loughner are likely.
He is next set to appear in court Monday in Phoenix.
"I don't think we're ever going to fully understand the whys and the how and, you know, the reason for what happened on the 8th of January," Kelly told reporters. "It's a loss of innocent life. The injury of a dozen people, the death of a 9-year-old girl, a federal judge and the serious traumatic injury to my wife Gabrielle -- we'll never fully understand that."
CNN's Paul Vercammen, Susan Candiotti and Roni Selig contributed to this report.