Is it permissible for me to propose to a working woman while I am unemployed?

There is no blame upon you for proposing before you find a job. If the woman accepts you, there is no impediment to marriage in this situation, based on Ibn Qudamah's permissibility of marriage for both those able and unable to provide for it, citing the Prophet's (peace be upon him) marriage to one who could only find an iron ring. It is incumbent upon those who cannot marry to seek chastity until Allah enriches them. You must strive diligently to find a lawful job, rely on Allah, and have a good opinion of Him.