How can I help my girlfriend?

You're probably not going to like my answer.

Your question says a lot about what YOU want rather than what she wants or what may be best for her. Sometimes, what's best for a person is the hardest thing to do, and may be completely opposite of what YOU want.

Addictions don't happen in a vacuum. If you've had any experience with addicts at all, then I'm sure you've heard the term "enabler". A lot of the times, when people think they're "helping", they're actually enabling the addict to continue their self-destructive behavior. Tough love and clear boundaries are needed in a lot of situations, but especially with addictions. Family and friends are often the biggest contributing factor to someone choosing to use/drink, continuing to do so, or relapsing back into it.

You said she recently quit. You said she is depressed. She wants to move. When a person receives counseling for addictions, they are encouraged to make changes like this. They need to break the habit, and this means removing people from their lives at times. It means moving to new locations. Anything that may trigger a relapse needs to be identified and removed. Not only that, but the addict needs to do a lot of personal reflection to figure out WHY they use/drink in the first place, and not only break the physical addiction to it, but deal with whatever is the root cause that led them to use in the first place. She may need some time alone to figure out who she is as a person, time to make some decisions for herself and do what she needs to do to be healthy.

Don't pressure her to stay. Let her have the freedom to do what she needs to do. If she stays, the decision needs to be hers and hers alone. It doesn't need to be made under pressure. That will only lead to resentment. Support her, but don't try to change her or make her do anything, especially for selfish reasons. Let her go. It sounds like she needs some time to focus on herself right now. It wouldn't be a bad idea for you to do the same.

 Changing scenery often helps in recovery. Could you move with her?  Moving could help her depression also. Is she also open to therapy?   Being supportive is one way to help her, and allowing her the space and ways to heal that suits her best.  

People often have very different values and opinions when they are drinking excessively and when they stop drinking so much.

Did the two of you share drinking as an activity?  If yes, then did you stop drinking too?

Often when partners meet each other as drinking buddies when one gets sober, the relationship ends.  Once the terms of any relationship changes, one possibility is that it dissolves.

The best way to go is to start the conversation of what you genuinely want.  This is the only way she'll really know your thoughts.

Ask her to give serious consideration and discussion over at least a few weeks or months, to moving away from you.  This is a fair request since you are in a relationship.

If she's changed so much by giving up drinking, which is possible, that she no longer wants to be in relationship to you, then you are better off being without a drinking gf, even if the truth she delivers is a hurtful one.

  After stopping the abuse of alcohol, depressive symptoms are common. She may benefit from exploring why she wants to move and see if she would still want to move if she did not feel depressed. 12 step meetings can also be helpful.