I made a mistake it was not the first martyr, but a woman named Nusaybah bint Ka’ab that fought according to some references (they may be ahadeeth from ahlulsunnah correct me in that case) in the battle of Uhud. My question was not if it was wajib but is it allowed? So can she if she wants it go to war to fight?

It is not not wajib but if they want and Masoom allows them then there is no problem