All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no doubt that what you did with that non-Mahram woman is forbidden. So, both of you are obliged to repent to Allaah. Furthermore, you must immediately end all relations with her in order to block the doors of evil and temptation.
If you want to marry her, you may do so because what happened between both of you is not an impediment that prevents you from marrying each other. Allaah has legislated marrying more than one wife, as He Says (what means): {…then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one….}[Quran 4:3]
Therefore, there is no impediment that prevents you from marrying her. Besides, it is reported that the Prophet said: "The best solution for two people who love each other is marriage." [Ibn Maajah]
Therefore, the best remedy for the one who loves a girl and she loves him is to marry her.
Allaah Knows best.