OK, my initial reaction was that she was assigned Farragut, since Uhura was mentioned as being assigned there, then someone was assigned to the Antares. Gaila turned to Uhura with a huge smile which makes me think she was assigned to Farragut too, and she was happy to be with her buddy and roomate Uhura. Of course, Uhura snapped the whip and got Spock to change her assignment, a little fact that annoyed me, but not so much.
So, I think she was on Farragut or Antares.
Captain Kirk to the Enterprise in "The Naked Time":
"I'll never lose you!"