(CNN) -- Wherever she goes, Nadine Devilme carries with her a small bag decorated with yellow ducks and filled with her most treasured possessions: photographs of herself pregnant, a tiny blue Bible inscribed with her infant daughter's name, her daughter's records from the pediatrician, and the dried up remnants of her umbilical cord.
This is all she has to remind her of her 4-month-old baby, Jenny Alexis, who was buried in the rubble of their home in Port-au-Prince, says Devilme.
"I can't sleep at night," she says in Creole through a translator. "This is all that I have. She's my only child."
Her daughter isn't dead, Devilme says. Jenny is in Florida, and she and her husband, Junior Alexis, have spent the past seven weeks trying to get her back, begging for a DNA test to prove the baby is their daughter, she says.
A short ride to Miami, a long ride home
On January 12, the day the giant earthquake struck Haiti, Devilme says she was at home and knocked unconscious. She was taken to a hospital, and when she awoke a few hours later, she urged her husband to go home and search for Jenny.
Alexis searched through the broken rubble every day for four days, but found nothing. Then the couple says on the fifth day, January 16, witnesses saw a cleanup crew rescue Jenny from the rubble. She reportedly was found in the arms of her baby sitter, who was dead. The witnesses got word to Devilme, who was in the hospital with her own injuries.
Rescuers apparently assumed the baby was an orphan and whisked her away to a different hospital in Port-au-Prince, one run by the University of Miami and Project Medishare, where a team of pediatricians worked desperately to keep her alive.
With several broken ribs, the baby was having trouble breathing. The doctors stabilized her, and a few hours after the baby's rescue, a United Nations truck took her to a plane that was minutes away from leaving for Miami, Florida.
"I told the ambulance driver if she got there in time, we'd name the baby after her," says Dr. Arthur Fournier, a University of Miami physician working at the hospital.
The driver, Patricia, did make it on time and thereafter, doctors at Jackson Memorial Hospital in Miami referred to the infant by that name.
"Her name isn't Patricia," Devilme says. "Her name is Jenny."
Devilme says the friend who told her of Jenny's rescue didn't know where the baby had been taken. By the time she found out , the baby had already been flown to Miami, Devilme says.
Devilme and Alexis say it was "God's will" that Jenny went to Miami, as she might not have survived if she'd stayed in Haiti.
"We're happy they're helping our baby," Alexis says. "But we need our baby back."
Test results could take two weeks
The couple, now living in a tent near their destroyed home, say they've received regular updates from the Red Cross, and the baby has been discharged from the hospital, and is now in good health and living in foster care in Florida.
They've been told a Red Cross car will arrive on Tuesday at 7:30 a.m. to take them for a DNA test, which they hope will prove the baby is theirs. The test was requested by Mark LaPointe, a lawyer appointed by the state of Florida to represent the baby.
A Florida state official who asked not to be named said he fully expects the DNA test to prove Nadine and Junior are the parents. Devilme and Alexis say they're grateful to finally take the test, but they don't understand why it has taken so long.
The DNA tests have taken more than a month because of logistical difficulties getting the test to Haiti and because of a legal dispute over whether the baby should become a ward of the state of Florida or a ward of the federal government, says Mark Riordan, a spokesman for the Florida Department of Children and Families.
It will take "two weeks max" to do the testing, and if the DNA matches, the reunification process will begin, Riordan says.
Devilme and Alexis say if it's proven they're the parents, they don't necessarily want their baby back immediately, since they're told her ribs aren't fully healed, and they think it would be difficult for her to recuperate in the tent.
While they await Tuesday's test, Devilme has the small blue Bible to remind her of her daughter. On the first page is written "Jenny Alexis" and the infant's date and time of birth, November 1, 2009, at 10 p.m.
Her husband carries a black and white copy of a photograph of the baby in her crib at Jackson Memorial Hospital. He says Delphine Marce, a Red Cross worker, gave him the photo.
"I look at the picture and I cry," he says. "That's all I have is this picture."
Is it possible, a reporter asks, that this isn't their baby? That in the post-earthquake chaos their baby was confused with another?
"Oh no, absolutely not," Devilme says. "I've seen the pictures. That's our baby."
CNN's John Bonifield contributed to this report.