Six milligrams is high dose. I was on a much higher dose of Klonopin.
Do consult your doctor on tapering. Benzos are normally prescribed for a few days during alcohol detox. Drinking and taking Xanax for an extended period of time will set you up for a world of hurt.
I do question any doctor who prescribed Xanax to a recovering or struggling alcoholic for an extended period of time at that dosage.
If you have been taking the Xanax for many months and the doctor just tells you to stop, get a second opinion.