I still have vivid drinking dreams halfway through my second year. I'm always glad that they turn out just to have been dreams. I see them as random flashbacks, they don't particularly bother me. Day to day, my obsession is gone. But I still get the dreams from time to time.
Oddly, I can still get physical flashbacks at times to drinking. I think I can smell alcohol, or I have a taste in my mouth like alcohol. I have no idea what causes it - I can be feeling fine, not thinking about anything related to drinking. Then, sudden flashback.
Congrats on completing your first month and they say that dreams can be symbols
so maybe it is of your sobriety, an interesting twist.