Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is reported in an authentic Hadith that the Prophet (Sallallahu Alaihi wa Sallam) said: "Each one of you is a caretaker and each caretaker is responsible for what is under his guardianship." Al-Bukhari and Muslim.
Now since this girl is under your guardianship, you should take care of her, teach her the right religion of Islam, oblige her to adhere to legal Islamic Hijab. You must also guard her from being involved in any Haram (forbidden) act such as traveling without being accompanied by Mahram (non-marriageable man) or mixing with the opposite sex or staying in seclusion with alien men, etc. What she has done might have been due to some neglect from your side as you might have fallen short of fulfilling your responsibilities in the best way. You should now repent to Allah and do your best to make right any previous short comings.
Know also that you should cover her transgression. Neither you nor your daughter should ever inform anyone of what happened. Malik reported that the Prophet (Sallallahu Alaihi wa Sallam) said: "whoever happens to fall in any of these filthy things (sins) he/she should conceal him/herself with the cover of Allah."
You should also make it clear to her that if she happens to become pregnant due to such an act, it will be unlawful for her to abort as doing so is killing a soul with no legal right. Finally, know that Hudud (Shariah retributive punishments) can not be executed except by the Muslim ruler or someone acting on his behalf. So, no one should undertake that whether a father, a husband, or someone else. In fact, this right is exclusively for the ruler or his representative.
Allah knows best.