Well, you are only in early stages of your relationship, and you have confronted her with the problem.. and I do believe its a problem and I think you know it is as well.
I have a mother with a drinking problem, I had to stop seeing her and talking to her for a while there.. because with it comes the paranoia, conflicts about everything. And its just recently that we are talking again, I have seen a change in her.
I thought my partner had a drinking problem and in a way he did.. he went to AA, and I went to Alnon, and for me, it helped a great deal, that other people was experiencing and feeling everything that I was... about the drinkers in my family and my partner...
He like me, had to move away from his mother, he had to deal with helping himself. People will ask for help if they want it and know they need it.
I know you don't want to be cruel and careless to your partner, you love her.. go see some-one together, see how she reacts? And if nothing has changed, then you have done all that you can.
You have lived with it, you need to break your own life circle. I know it sounds hard. But you need to be happy too.
My partner has been through hell and back, he lives with me four days a week and with his dad the other days.. he is helping himself and I can see how much he loves me and how much work he has done. Our goal is to move in together permanently and have a family, although I have 3 children.. that became an issue too, BUT my point is that he is willing to do anything.. and that means a lot to me..
Give it your last one shot, and if it doesn't work... move on
Hope it works out for you...