Should A Daughter Be Asked to Keep An Adult Secret?

I admire you for facing your difficulty and support you in your decision to stop drinking. Now that you have stood up and took responsibility for your drinking, now you need to stand up and be a good father.
Asking your daughter to keep this secret does indeed do harm. Your daughter needs you as a responsible father. Keeping your secret will stress her, permanently change your relationship with her, and set her up to enable a future alcoholic, herself or her significant other. It will also taint her understanding about what it means to be a good parent and partner.
You need to talk to your wife, tell her of your decision to quit drinking, of your indiscretion and your initial decision to ask your daughter to keep the secret. Then get into counseling with your wife and daughter. The counselor should be able to screen you for alcoholism. AA for you and Alanon for your wife and Alateen for your daughter would be good options. If you are still unable to quit, chemical dependency treatment is necessary.
Your honesty will repair much of the damage with your daughter. Your wife will be angry, but your decision to come forward to save your daughter the pain of keeping a secret should get her attention that you are serious about making changes.
The repair will be long and painful. But it is well worth what it will do for your daughter. I wish you the very best.