This story could have been a lot better than it was. It is not -impossible- to show a character as normally put together as Hawkeye in the throes of depression and suicide, but it requires a lot more development than you gave it. You needed to show us how she was slipping, give us examples (other than the one you gave us at the end), of how she didn't -feel- appreciated, whether that was reality of not. You could do that a number of ways, POV's of other characters, flashbacks, etc.
Watch your dialouge as well. You managed to convey the thought process of a depressed person quite well, but you missed easy chances to add description, mood, and general depth by not describing what your characters were -doing- as they said the words. All emotions have physical manifestations; show them to us.
You have a fairly decent grasp of grammar, which helped. Your biggest problem is that Hawkeye was quite simply out of character. I'll reiterate this, if you want to take a character as stable as Hawkeye and explore themes of depression and suicide, it takes a lot more work, than say, if you were to do the same with Mustang, who's established a precedence for that type of behavior.
I don't criticize to be mean. This story had a lot of potential, but you have to take the time to develop it. Good luck with your next piece.