I met my boyfriend at the dojo. Then we broke up and it was a bit awkward... luckily, he quit. His presence never discouraged me from training there though. So keep in mind that there is a possiblility that you two may not work out and that things could get a little strange.
That same dojo is also where I met my husband!
Apparently, I have a thing for martial artists.... haha. We are now happily married and I think that it is great that we are both so passionate about the same thing. A relationship that grows from friendship is usually very special.
I say train and just let things happen. If it is meant to be, then it is meant to be. Be careful though, I know some dojo's have rules about dating students or a teacher (like my husband was when we started dating). If you two do end up dating, I would suggest not working together (or at least not too often).
My husband and I try not to work with each other (but eventually do if there are less people in class). In fact, just this weekend, Sensei purposely put us together. We found that a little strange. Sensei at our new dojo doesn't seem to mind us working together as much as the sensei of our past dojo. Good luck!
Sorry if I am missing t's in my words.... the keyboard is messed up. I hope I caught them as I went!