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.
The most important thing that a person has to consider in a woman when he wants to get married is her religion and moral conduct. The Prophet said: "Choose the religious one, you will prosper". [Al-Bukhari and Muslim] Natural differences are not considered [in religion when getting married] and a good conduct is not enough without being religious.
Wearing Hijab is something that Allaah has prescribed on Muslim women, Allaah says (which means): {O Prophet! Tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments.}[Quran 33:59]. By wearing it, a woman protects her religion, honour and dignity. For more details please refer to Fatwa: 89972.
If what you mean by her not wearing Hijab, is not covering her head or other parts of her body that must be covered according to the consensus of the scholars then it is more appropriate for you not to marry this woman. First, you should try to convince her that wearing Hijab is obligatory on her. If she is convinced and wears it, then you may take the initiative to marry her after performing Istikhaarah prayer. But if she is not convinced and refuses to wear it, then there is no good for you in marrying her. Since she is neglectful of the Right of Allaah on her, she would be neglectful of the right of her husband. We think that you are more in need of a righteous wife who would remind you of your religious obligations and help you perform them.
However, if you mean by her not wearing Hijab that she does not cover her face, then you can marry her and endeavour to convince her to cover her face, as this is a controversial issue among the scholars.
It should be noted that the reality of Istikhaarah prayer is putting the matter is Allaah's Hands to choose for you what is best and more beneficial. The outcome of Istikhaarah is nothing but good, Inshaa' Allaah. However, its result could be contrary to one's desires. Nonetheless, having a weak faith does not prevent someone from performing Istikhaarah prayer as Allaah accepts the supplication of a non-Muslim if he is sincere in his supplication, so how is it that He will not respond to a disobedient Muslim, Allaah says (which means): {…and they assume that they are surrounded [i.e. doomed], supplicating Allah sincere to Him in religion, "If You should save us from this, we will surely be among the thankful." But when He saves them, at once they commit injustice upon the earth without right.}[Quran 10:22-23].
Finally, we advise you to avoid being negligent or disobedient, as these weaken the faith. Besides, you have to be keen on mentioning Allaah and performing acts of obedience and keeping company with righteous people, as these are the reasons of strengthening one's faith. Moreover, you have to avoid establishing any relationship with this woman outside of marriage as this is not permissible and it is one of the means that lead to committing fornication and/or adultery, we seek refuge in Allaah from that. What is permissible in your situation is to ask her hand for marriage if she is a righteous and religious woman as we have previously mentioned, if her parents agree, all the best, otherwise you have to stop thinking about her, taking into account that a woman in the process of engagement is a marriageable woman so you are not allowed to stay in seclusion with her or look at her or talk to her without a need.
Allaah knows best.