Can a jamaican woman marry an american woman and it be recognized in the states?

I am an American woman, I want to ask my Jamaican girlfriend to marry me. She is in the states on a visa. If we elope will she be able to stay here with me? I understand that men and women do it all the time. I have tried to look at the laws but cannot seem to find the right ones. Someone help she has 2 1/2 months left on her visa and I want her to marry me now! Also, what stated allow gay marriage? and Does anyone know what colors would look good for the wedding?