Well, when I reached Second Lieutenant at level 48, the game told be that Personal Housing has been unlocked (with the fanfare music and big yellow lettering across the center of the screen that it uses on feature unlocks). And the next time I entered a housing area, it repeated that statement (though smaller and by the chat box this time). I haven't tried actually buying one as I'm still saving up money, but I'm pretty sure I could if I had the gil for it.