Q (also refered to as the Female Q) was a member of the Q Continuum who, during the Q Civil War, opposed changes of the kind advocated by her former boyfriend, Q. During the war, she recruited Doctor Selar of the USS Enterprise to serve as both a medic, and to provide a logical, objective viewpoint of the conflict. To end the war, Q agreed to conceive a child with Q. Q gave birth shortly after the conception, with Selar serving as midwife. (NF short story: "'Q'uandry")
External Link
Q (female) article at Memory Alpha, the canon Star Trek wiki.