We can’t tell you whom you should and should not date.
With that being said, you should always do what is best for your spiritual well being. Your relationship with God should always come before all other relationships. This includes, friends, family, and even spouses. God is always first.
So you have to decide if this person is going to hurt your relationship with God. If so, you should avoid that person. But there is certainly no requirement that a person must be Catholic or even believe in God to date them. In fact, just the opposite, perhaps God is working through you to be an example and draw this person toward God and His church.
You should approach this decision like any other, with prayer.
Also, you should consider long term, should the relationship last for an extended amount of time. If this person never believes in God is that something you can handle and handle without damaging your own spirituality? If you are Catholic it would be required by the church that you are married in the church and promise to raise your kids Catholic. Is that something she would be prepared to do?