If it was me I would say I stopped drinking after Christmas/New Year/whenever your sobriety date was for health reasons. Say you are feeling much better physically and mentally for having stopped and don't want to drink. So you won't be going out as it would be too tempting. Then ask her out for lunch/coffee/gym one day so you and she can catch up without alcohol.
If she is a true friend she will respect your position, not push the issue and look forward to meeting you for lunch to catch up. If she harasses you, pressures you, makes fun of you she is a drinking buddy,doesn't have your best interests at heart and reconsider your friendship. remember, if she has a problem it is HER problem ,not yours.
I also agree with Xune-this is a private issue,I do not broadcast my problems to others either as consider it my private business.good luck