The beginning of your logline delays the start of the story by having this: "In a dark and dangerous world with no sun and most of the people gone," before it tells what happens.
Better to jump into the action sooner rather than later because the point of the logline is to describe the plot above all.
So if you were to remove the first sentence it would read:
"A terrified young girl must find her sister before she dies from the cold, lack of oxygen or gets killed by survivors gone mad?
However this is confusing because the environment is not mentioned and there is no inciting incident.
Also the MC flaw is too generic and therefore does't relate to the specific obstacle she will face It begs the question; terrified of what?
Her depression is not a flaw it is a condition and a result of her circumstance I would expect most people to be depressed if they were in her shoes? It is nothing she can necessarily over come and I think pales in comparison to her over coming for example: nytcophobia or agoraphobia.
In essence the lack of oxygen, sun and general danger should come across from the setting description as it plays such a heavy part in this concept but not elaborated on. Let the description engage the readers imagination and make them want to know more rather than specify exactly the nature of this dreadful place.
I think Richiev gave a good re draft bellow the brevity in the setting description helps the reader understand the stakes. I would recommend perhaps an even shorter description such as: post apocalyptic, but that comes down to personal taste. As long as it sets up a setting that could have all the needed "bad things" to make MC's goal harder (and therefore more interesting) to achieve.