Sorry you're having a rough time brother. But I think you have to ask yourself clearly what you want with her. And then look at her very clearly and ask yourself if she can give you what you're looking for.
First of all, depressed people in your life are always going to be a rough ride. They will make you sweat as you try to walk the line between leadership and mental support, not pushing them too hard or too little, trying to be empathetic but not an emotional tampon. Their tendency to feel victimized is a constant threat to your ability to express yourself naturally, honestly, and dominantly. Taking on a depressed girlfriend is not something to take lightly, and you must avoid falling into the pitfall of thinking in terms of 'fixing' her - the beginning of a relationship is usually the easiest time you will have, and breaking up with her years down the line after she's become dependent on you can feel like you're sending her off a cliff.
I may be wrong about this, and I hope I'm not being too blunt here, but it sounds to me like there is a bit of neediness on your part. That you may not like her as much as you think you do, but you feel like you have to accept a lot of negatives because you don't think you'll find another girl as hot. If that's the case, not only is this a very bad frame for you to operate in, but she will feel it, and she will resent you for it.
In your whole post, nowhere did I see anything about her having to prove herself to you, passing your tests and bending over backward to please you and fulfill your expectations. Instead she seems to think she is a casual fling who you got attached to, who sometimes you act like a boyfriend toward. If that in itself isn't enough to tell her you aren't the sort of man she's looking for (since women, for the long term, respect guys who manage their own life and relationships carefully) then she's certainly going to start prodding you very hard to clarify things one way or the other. But to do so now would be to hand her the frame and reins of the relationship, since it would be advancing at her will.
You have only two options, in my opinion: a) break up with her or b) reset the frame as your own - tell her you got lazy but from now on you want to see improvements X, Y, and Z on her part, and that the relationship will proceed based on how things go. Examples: she has to get a job, she has to stop sitting around all day feeling sorry for herself, she has to stop doing <insert something you really hate>, she has to <insert something you really want her to do>. Make her either rise to the occasion to become your first-choice, ideal girl, or leave.
But do not bother to do any of that unless you really are open to something more with her, or else you're wasting both your times.
Hope this helps!
