I would never date a drinker. Since you mentioned she doesn’t feel the same way as you, I assume you’ve spoken to her about your concerns? As someone who hasn’t gone on a date in his life as of yet, I can’t give real relationship advice, but I will say this. I don’t think your feelings on alcohol are a flaw of yours. If you hate alcohol because of your experiences with an alcoholic father, that’s a completely understandable and valid reason to feel that way. She should be able to understand that at the very least, even if she doesn’t think she’ll develop a problem. Your concern is realistic.
That said, I wouldn’t know the first thing about resolving this kind of problem. If I could help it I would never let myself get into a situation like this, but if I did, I don’t know what I could do other than ask her to stop. I’m definitely not saying you should do this, but if it were me and she chose alcohol over me, I’d probably walk away from the relationship.
I hope things work out for you.