A young girl accepted Islam with her free will but she is dependent on her family, so is it compulsory for her to follow the rulings of Shari'a?

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.

We thank Allah and offer you our best congratulations for being a Muslim, and we ask Allah to increase you in faith, to please you and make it easy for you.
Then, it is your duty as a Muslim to establish rites of Islam and to put its Teachings into practice according to one's ability as long as one is pubescent and sensible, even if one lives in a non-Muslim country or with non-Muslim family. One has to depart non-Muslim country if he can. Check our Fatwa:81642 in this concern.
As for residence with your family, we state that if your can leave them to live alone or with the Muslim community, without causing any worldly or religious harm to you, then, you should do so that you can practise Islam freely, completely and safely. If you cannot do so mentioned above, that you are to stay with your family and you are to perform your religious duties alone, in your room, for example.
Here, we inform you that our answer depends on your question, which is not clear. So, if you need to ask about something else or you need more information, feel free and send your question in English.
Allah knows best.