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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Indeed you did well in being keen to preserve your chastity, and we ask Allaah to protect you [from evil and illegal sexual relationships] throughout your life.
In general, it is known that a girl, at this age, is not usually desired for sexual relationship, and a person is not attracted to her in the same way he would be attracted to an adult woman, however, if one feels that he desires her for sexual relationship then he is not permitted to touch her or look at her with a desire and the like. Rather, he should treat her like a marriageable woman, as looking or touching with a desire is a kind of Zina (i.e. fornication or adultery). The Prophet said: "Allaah has written for the child of Aadam his/her share of Zina (fornication and adultery) which he/ she commits inevitably. The Zina of the eye is the sight (i.e. to gaze at what is forbidden), the Zina of the ears is the hearing (i.e. listening to what is forbidden), the Zina of the tongue is the speech (i.e. saying what is forbidden), the Zina of the hand is the touching (i.e. illicit touching), the Zina of the feet is the walking (i.e. to forbidden places) and the heart desires and wishes, while the private part ratifies that or denies it." [Muslim]
We fear that the feelings that you have towards this girl is an attempt from the devil to lure you into an illicit relationship, so you should avoid this matter, and you are obliged to avoid it if you have any desires when talking to her and the like. As regards the matter of her cultivation, it is her parents who should fulfil this task; and you mentioned that her parents are pious people. Nonetheless, if she is brought up according to religious principles and righteousness, and it is predestined for you to marry her, then this is good. You are allowed to ask her for marriage and conduct a marriage contract with her. Imaam Al-Bukhari reported that the Prophet married 'Aa'ishah when she was six years old, and he consummated the marriage with her when she was nine. Nonetheless, you may choose not to do anything until she grows up to make sure that she is religious and has a good moral conduct.
Allaah Knows best.