Is it permissible to propose to a girl who used to be immodestly dressed (mutabarrijah) and then wore the hijab at a later age (19 years old), and is now righteous?

If the girl is religious, of good character, and upright, then proposing to her and marrying her is religiously desirable, for the Prophet, peace and blessings be upon him, said: "Attain the religious woman; may your hands be soiled." Her being unveiled previously does not prevent marrying her, for repentance demolishes what came before it, and the best of sinners are those who repent. You should perform Istikhara to entrust your affair to Allah, so He may choose what is best for you.