While I absolutely wish you luck, forewarned is forearmed, so here goes:
a) one month sober is a good start, but still does not mean anything. It takes 3-6 months at least to ‘get out of the fog’ and for the person in recovery to actually start seeing clearly and hopefully redouble his/her efforts to get out of this mess. After one year you can start getting your hopes up, after two years you can cautiously breathe a sigh of relief - in one month I’ll be 3 years in, trust me, I know what I’m talking about.
b) moderation does not come into the picture. Even one drink restarts the clock.
c) if you hear after one month ‘I am healed now, I can drink socially’ you can consider the effort failed.
Sorry if this all sounds very harsh, but this does not only reflect my own experience, but the combined experience of hundreds and hundreds of stories on the SR newcomers section. So yes, go ahead and give it another try, but stay alert for any red flags and make sure you don’t get hurt even more. Protect yourself and learn as much about this disease as you can. Happy to answer any questions you might have!