AFAIK the only way you can do this is by using the fantasia potion you get as a 30 day subscription reward thingie: http://ffxiv.gamerescape.com/wiki/Fantasia
lets you completely recreate your character including race, gender, diety, etc by going through the character creation process again. only thing you cant change is your name :)
edit: here's more details, thanks to Valkayree's post here
Edited, Oct 5th 2013 4:58am by chillpickle
Fantasia grants you a single opportunity to edit your character.
You will be allowed to change your race, gender, appearance, date of birth, and patron deity.
*Your starting class and name cannot be changed.
Changing Your Appearance
After using Fantasia, you will be allowed to change your appearance in the character creation screen upon your next login.
At the character selection screen, right click the character or press square to proceed to the character creator.
* Before using Fantasia, you must remove all equipment except for your main hand.
- If you do not choose to change your appearance at the character selection screen, you will not lose the effect of Fantasia.
- When you have finished using the character creator, Fantasia will be consumed even if there are no changes in your character's appearance.
- The appearance change granted by Fantasia will not be saved until you have completed using the character creator.