You need to be really careful about this. It can turn into a situation where you end up becoming her caregiver. For a while, you would get the satisfaction of being able to take care of somebody else's problems. She would get to lean on somebody else instead of handling her own problems. That's not what a couple's relationship should be about. Eventually you would both want a more equal relationship. There is also the problem that it would be harder for her if you guys broke up since she would have become dependent on you.
If you want to pursue this, first you need to make sure that she is interested in fixing herself. It can happen to anyone, but somebody who isn't interested in fixing the problem won't make a good partner. Second, you need to be sure you aren't looking to be the hero. If you just want to be there for her as a friend, that's fine. But if you're finding yourself plotting ways to get her out of her depression, or dreaming about being the one who gets her out of it, or thinking about her depression more than other aspects of her, then you probably shouldn't be getting into this. If that's not the case, then give it a shot, but take things slow before getting too serious.
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy