I would deal with it the way you did. Time out, ignore it. Then once she is back to her old self i would sit down and tell her that her saying she hated you really hurt you and made you feel really sad. I think you need to let her know this so she knows she is hurting you by saying it. I honestly dont think she meant it.. she wouldnt know the real meaning of it at 3.. it was just a spur of the moment anger thing.

Best of luck.