every wiki page say she a sun
http://ffxiv.gamerescape.com/wiki/F'lhaminn
So yes she is a sun keeper so there you go.
Here info on the sun
Due to their exposure to light, the pupils of a "Seeker of the Sun" are vertically aligned slits with irises faintly colored. It is also not uncommon for their eyes to be disparately colored from birth, a trait considered auspicious amongst their kind.'
and the moon
in contrast, due to their exposure to darkness, the pupils of a "Keeper of the Moon" are large and round, with very little iris exposure. They are distinguishable from their diurnal cousins by their darker fur, larger ears, rounder eyes, more pronounced canines, and longer, skinnier tails.
I think you just looking into it way to much just becuase her eyes does not fit in to the plot story does not mean she not a seeker of the sun it just a mistake by SE or she just does not have what most seeker of the sun have for w/e reason. It's not uncommon for people to not get the trades from there clan members.