The highest success rates in bone marrow transplants for leukemia are done when children are in remission, but so far, Jasmina's tumor has been resistant to chemotherapy. "Without a low level of cancer cells, the chance of a cure is remote," her doctor told ABCNews.com.
"We'll go to transplant, but we don't know a more successful option," said Carroll. "Chemo alone is unable to cure this."
Doctors have found "a lot of promising matches," which will require more "granular" analysis to see if they can be given to Jasmina, according to Carroll. But time is running out.
Her doctors are also looking for a cord blood donor, which can be effective in children. In some cases, the experimental procedure can yield 50 to 60 percent survival rates, according to Dr. Gary Kleiner, pediatric immunologist, University of Miami School of Medicine.
"Cord blood has an advantage over marrow for minorities," said Kleiner, who is not treating Jasmina. "Marrow has to be an exact match. Cord can be a mismatch."
Cord blood, taken from placental tissue, is also quicker if a match is found, as it is frozen and does not require live donation.
"We don't know why [it works], but the T cells in cord blood are less mature," he said. "We think the cells are more naive. But it's only good for children and not adults."
Meanwhile, Jasmina's mother vacillates between hope and despair. "One doctor is not optimistic and the other doctor is. One says the glass is half empty and the other half full."
Jasmina's doctors agree the challenge to cure Jasmina is daunting.
"I'm the optimistic one," said Carroll. "We know a cure is remote, but we haven't taken away any hope."
But it's Jasmina's spirit that makes her fight so inspiring.
"Despite the aggressive chemotherapy, she has sailed through this," said Carroll. "In my career I've never seen anything like this. She is playing and zipping around and animated. We're delighted."
"Obviously, children are smaller and more fragile, but they have an enthusiasm for life," he said. "They live for the day and take one day at a time and it gets them through. The rest of us worry about what's coming down the line."
As for Jasmina's mother, "All I can say is I have great friends, incredible support -- fantastic friends."
WABC-TV's Carolina Leid contributed to this report