I don't think your friend is an alcoholic. You only go out with her once a month, maybe when she's around you she feels safe enough to drink alcohol. If you are worried that she might be an alcoholic you should try and get together in a place where there are no drinks. Maybe you could go to the cinema, where they don't really sell alcohol. If she brings alcohol to the cinema she might have a drinking problem. Or you can ask her friends or co-workers who see her daily, but maybe she will find out and get mad at you. Dealing with people who are addicted to alcohol is very tricky.
I think if you only catch up once a month it's difficult to work out whether she has an abusive relationship with drink (as you see it) or is an actual alcoholic. Her getting drunk every time you meet doesn't necessarily mean that she's an alcoholic, even if it does suggest a less than balanced relationship with drink. I'd try to find out a bit more about her drink patterns in general, rather than assume that how she is on these isolated occasions represents the bigger picture.