Is it right that a recent Ger date a Non-Jew?

I recently officially became Jewish. I am Orthodox and Shomer Shabbos/Kashrut. One week after my Mikvah I met the most amazing Non-Jewish girl in the world. Although at first we were just friends we have developed feelings for each other and now we want to date. I am afraid to ask my Rabbi as I know he would be upset that I am dating goyim so soon even after I said that I wanted to marry a Jewish girl in my Beis Din. This isn't something I planned and I never in a million years would have sought this girl out. What should I do? Should I date her and just see where it goes? Do I have to end it now? Is it fair to create an interfaith relationship as a ger.....Should I even go to my Rabbi with this question? What should I do? I feel so lost. Finding Judaism was the greatest thing that ever happened to me. Now I feel so confused.