In the first place, we would like to stress that sacrifice is considered an expression of thankfulness to
God, in relation to that historic event, when Prophet Abraham was ordered to offer his son in sacrifice.
It was a divine order, which both – the father and son – were ready to obey unquestioningly. However, the son’s life was spared and ransomed by a ram.
Offering of the sacrifice has become an annual celebration to commemorate the occasion and thank God for His favors. In this, it is a clear and direct admission of the link between Islam and the Father of all Prophets, Prophet Abraham (peace and blessings be upon him).
Dr. Rif`at Fawzi, former head of the department of Shari`ah at Cairo University, states the following: “First of all, I would like to stress that offering sacrifice on the Day of `Eid Al-Adha is a Prophetic Sunnah. It is not an abligatory act that is required of every Muslim. In this regard, I would like also to stress that a Muslim can be a committed Muslim without offering the animal sacrifice on the Days of `Eidul-Adha as the gate is open before all Muslims in all times and under all circumstances to improve their relationship with Allah by sticking to His Commads and the traditions of Prophet Muhammad (peace and blessings be upon him).
Having stated the above, I should stress here that the Sunnah is to slaughter an animal on the Days of `Eidul-Adha as by this the Muslim will be obeying Allah by following the tradition of both Prophet Abraham and Prophet Muhammad (peace and blessings be upon them both). The act of sacrifice itself is a symbol by which Muslims show that they are willing to give up some of their own benefits for the sake of obeying Allah. It is not intended, at all, to bring harm to animals or to slaughter as many of them on the Days of `Eidul-Adha. To the contrary, each Muslim offering the sacrifice on the Days of `Eidul-Adha is required to follow the Prophetic Sunnah from avoiding being cruel to animals, being merciful when slaughtering them, etc.
With the above in mind, offering the price of the sacrificial animal is not sufficient for one to fulfil this great Prophetic Sunnah. It can never be a compensation for the slaughtered animal. Thus, if you are interested in offering charity to the poor on the Day of `Eid to the poor, then it is okay but this act of charity can’t be equivalent to the sacrificial animal.”
In addition to the above, it should be clear that a Muslim should only marry from among Muslims. So, if this girl doesn’t covert to Islam, you will not be allowed to marry her. But, if she, out of conviction, embraces Islam, you then can marry her and lead a happy marital life based on Islam.