If you mean that she gets fatigued easily, before other members of the party, then yes, that is intended because of her aforementioned low constitution. If you mean that she is always fatigued, even after resting, then no, something's not right.
Has she cast any restoration spells? Casting restoration spells (lesser and greater) fatigues the caster, so that could be one reason aside from her low CON.
Comments
If you mean that she is always fatigued, even after resting, then no, something's not right.