On the street outside, people shout and loudspeakers squawk - the din of Muslim men marching past by the thousands, demanding a strong role for religion in the new Iraq.
With the fall of Saddam Hussein, al-Baghdadi, 23, says the future has never looked more hopeful. She speaks optimistically, like many young Iraqi women just old enough to be resentful but not broken by hardships and discrimination under Saddam.
On the other hand, al-Baghdadi concedes, a fear threatens to crush any hope: that men like the thousands marching outside will bring an extremist state - one that forces Iraqi women, among the region's most educated, to retreat to their homes.
"If an uneducated person comes in control, I'll have to leave Iraq," al-Baghdadi said. "I love my job too much." Around her, female colleagues nodded agreement.
Iraqi women, closer to equality than their counterparts in many neighboring countries, have an enormous amount to lose in a future Iraq.
Across the country, particularly in strongholds of the majority Shiite Muslim sect like Najaf and Karbala, calls are rising for Iraq to become an Islamic state. That would mean sharia, or Muslim law, would be implemented, and it has been interpreted in many nations as significantly curtailing women's roles in public life.
In a country whose male population has been winnowed by wars, women make up at least 55 percent of the population. Iraqi women routinely study for up to two decades, taking professional jobs ranging from engineering to teaching to medical care.
Saddam's regime went through the motions of equality. Girls went to Baath Party gun-training camps. Women held high posts in the party and government.
Recent years, though, saw increasing dips in the seemingly level ground for women. Saddam catered more and more to Islamic fundamentalists as wars, sanctions and corruption eroded Iraq's middle class and as the Iraqi leader courted support from the religious establishment and traditionalist tribes.
One edict banned women from traveling outside Iraq without a male relative. Women interviewed said the extra financial burden effectively ended foreign travel for them.
Professional women said Saddam's power structure shut them out: Young men with lower test scores beat out women for prize slots in universities. Harassment made it impossible for many women to hold a department-head position.
"I lost my self-confidence," Sahar, a 39-year-old ex-engineer with sad eyes and wispy hair, said from the refuge of her family's walled yard.
Sahar, who spoke on condition her last name not be used, quit work in 1995, driven out by pressure to take bribes and harassment by male colleagues.
"It's so difficult now for me even to think of looking for another job," she said.
Now, like many Iraqis, she and her husband yearn to take their 13-year-old daughter and 12-year-old son out of Iraq, to escape the lawlessness and prospect of fundamentalist religious rule.
"What concerns me these days is how to get out of here," says Sahar, whose family, as Christians, has added distrust of any Islamic state. "We have to leave."
"We are so tired of this life, so miserable. There are only thieves, killing and murder," said 35-year-old Kawther Mohammed, a mother of two, forced by her soldier husband's death in the Iran-Iraq war to make a living selling vegetable oil on the streets.
Life in Iraq "is a tragedy that cannot be separated. What is suffered by the men is suffered by the women," said 60-year-old Sabirha, a Shiite with traditional blue tribal markings on her face.
Sabirha, who had just six years of education, sat in her home surrounded by five daughters and daughters-in-law - all teachers or engineers with advanced degrees.
The women wore flowered pajamas. Baghdad's war-interrupted power meant they had electricity only in the early morning, so they stayed up all night to cook and clean while appliances worked.
It was another privation of war that concerned the household on this day, however. After 18 years of study, 42-year-old daughter Kareema's verbal examination for her master's degree had been set for the next day.
The examination was scheduled before the U.S. military invasion and capped her lifetime pursuit of a military engineering career. But now that the war is over, the exam seems unlikely to happen: The university has probably been looted, if not burned.
"I completed everything," Kareema said "Everything was done, except for tomorrow."
Asking if a visitor knew anything of the fate of the master's exam, she shrugged. For this family - with 12 members depending on a single taxi for income - the future is bleak.
"I think I will have no job," Kareema said. "I expect the worst. Worse than ever."
By Ellen Knickmeyer