Dana gave birth via emergency c-section at Bentley Hospital.
Dana's baby was delivered via emergency C-section despite Bentley Hospital not having the proper facilities. Her baby was then transported to Seattle Grace Mercy West Hospital, because she had a tracheoesophageal fistula, which was causing her to have trouble breathing. When Meredith and Alex came to get the baby, Dana tried to go with them, saying her baby didn't even have a name yet. Meredith reassured her, saying that they were taking her daughter to the best baby surgeon there is and she would come to Seattle to see her baby and then she could name her. ("Dark Was the Night")
Once at the hospital, Dana's daughter was taken into surgery to repair the fistula. The surgery was successful. ("Suddenly")
She has a daughter, delivered via emergency c-section at Bentley Hospital.