I think maybe the first thing is a talk about "what's normal?". And what would constitute a "drinking problem".
Getting a clear definition on both those will be a good start.
And to be sure. This isn't about who is right or wrong. It's about what society deems as normal.
She may well think 1 drink a week means a drinking problem. She can think what she wants. But she has to understand she's pretty much alone in thinking that. That may or may not make a difference, but it's important to establish I think what's "normal".
If it's a situation where she's not comfortable with you drinking at all, that's something to work through.
Why does she think that? Very often, it's something in her past she's seen. An alcoholic person she saw start with a single drink and turn into an alcoholic or something. Again, it's not going to be necessarily rational. But it's important to understand what you're dealing with.
Good luck there. I'd err on the side of clear over communication to work through it. Very often a counselor can be a big help here as it pulls in a (hopefully) objective voice. But I'd stress, don't go in with the idea the counselor is going to show her how wrong she is. Go in with the idea of hoping to find out what's going on.