Dating a non-believer or a non-Catholic: after my conversion, I would never do so. Simply because of the ultimate reason of dating: to discern if my God-given vocation is married life, and if so, if this is the right person, and if so, to lead her to heaven as she leads me to heaven, and to procreate and have children which are to become saints.
After my conversion, my entire viewpoint on dating changed radically. I only see trouble in dating a non-believer. I also see myself inflicting suffering on her, for there would be a great many things in my life (and, if we marry, in our family life) that she would not be able to comprehend and thus would feel hurt about. I do not think such a marriage would last (but I tend to be a pessimist).
This is what the Church officially teaches on the matter (and it matches what I had already mustered in my personal reflections, though in much better terms). Also please note that atheism, unlike agnosticism, is in fact a form of religious mindset, with its dogmas and its preachers.
Difference of confession between the spouses does not constitute an insurmountable obstacle for marriage, when they succeed in placing in common what they have received from their respective communities, and learn from each other the way in which each lives in fidelity to Christ. But the difficulties of mixed marriages must not be underestimated. …]
Differences about faith and the very notion of marriage, but also different religious mentalities, can become sources of tension in marriage, especially as regards the education of children. The temptation to religious indifference can then arise.
According to the law in force in the Latin Church, a mixed marriage needs for liceity the express permission of ecclesiastical authority. In case of disparity of cult an express dispensation from this impediment is required for the validity of the marriage. This permission or dispensation presupposes that both parties know and do not exclude the essential ends and properties of marriage; and furthermore that the Catholic party confirms the obligations, which have been made known to the non-Catholic party, of preserving his or her own faith and ensuring the baptism and education of the children in the Catholic Church.
In marriages with disparity of cult the Catholic spouse has a particular task: “For the unbelieving husband is consecrated through his wife, and the unbelieving wife is consecrated through her husband” (1 Cor. 7:16). It is a great joy for the Christian spouse and for the Church if this “consecration” should lead to the free conversion of the other spouse to the Christian faith. Sincere married love, the humble and patient practice of the family virtues, and perseverance in prayer can prepare the non-believing spouse to accept the grace of conversion.
Things are harder for you as a future wife, for “the husband is the head of the wife” in our faith. You would then be in a peculiar situation, forced constantly to obstacle your husband’s authority in order to have the religion respected, not only in regards to your children, but even in matters regarding your personal relationship. I am thinking of our beliefs regarding the sacredness of life and the fact that the marital embrace must always be open to life - something that a non-believer would probably not understand or not agree with, since the only option, natural family planning, does require quite a bit of work on the side of both.