I have always shot right handed. I used to be right eye dominate. An eye injury a few years ago made me switch to left eye dominate over night. I compensated right away and shoot as well as I ever did. In fact I never noticed any difference, even right away. The conclusion I came to was that even though I was right eye dominate, I believe I have always used my left eye as the dominate one. If you think about it a right handed shooter's right eye's vision is obstructed by the bow sight, fletching, string and bridge of nose where as the left eye has a wide open picture to the target.
This being said I am a purely an instinctive shooter and I believe that is why I didn't see a change in shooting. If you are using the arrow as a reference in any way, you may want to consider switching. I'd stay with right hand for a while though to see if it makes a difference before making a decision.
Chad