Concerning written rules you need to find out if any exist in your department, university etc. you will certainly not be the first or the only couple in this "situation". Unwritten rules are perhaps what you need to care more about and then I am actually not so much thinking about rules as such. First off, people know more about your relationship than you think. Or perhaps more precisely, they think they know more, in other words rumours and gossip might spread. so the advice is to be open about it and think about it as two adult persons in a relationship. It is your life, it is not a secret and most importantly, it is natural.
Regarding your work, you need to act professionally (like any other should). You need to help each other prioritize your respective careers and make sure your relationship can function despite the pressures graduate school inevitably involves. So in my opinion, you should worry more about balancing work and relationship so that you both can spend the time necessary to succeed. this means making sure the relationship does not directly or indirectly affect others on a professional level.