My girlfriend and I have been friends (3-4 years) for far longer than we've dated (just about a month). We started off as acquaintances online. Since then, she's developed a crush on me that's lasted well over a year. It hasn't gone away, even after I initially turned her down (for additional background, before I knew she had a crush on me, I had sex with a mutual friend of ours whom I no longer contact. She confessed later on that this stoked feelings of jealousy and desire toward me). However, her persistence convinced me that I couldn't go wrong giving her a try. It didn't seem like a risk, and we both communicated at length about what to expect from each other should we date. This is on top of the years we've spent being fairly close and open with one another, so it seemed like a no-brainer. I put hope in the possibility that, as we get closer, I would naturally come to match her level of affection. Given that she's very level-headed, if we felt like there wasn't chemistry, or that things weren't working out, then there would be no hard feelings should one of us decide to break it off.
To complicate things, my girlfriend doesn't respond well to sexuality. She goes out of her way to assure me that she isn't asexual and that she finds me attractive, but that she's very slow to open herself up physically. I believe her and have never held it against her, but have clarified that I expect things like sexuality in a relationship, and if it's not something she feels comfortable providing, then we have different needs and therefore shouldn't date.
She once told me that she wants our relationship to resemble child best friends, where physical and emotional intimacy isn't bound up in sexuality. When she asked me why it couldn't be that way, I said, "because I'm not a child" (more on this later).
After that conversation, though, she told me that, after some thinking, she had become comfortable with being sexually open with me. That was my only explicit barrier to a relationship, so soon after, we started dating. For context, I am her first boyfriend.
As it turns out, the last month and a half for the both of us have been turbulent. I've been busy moving out of my childhood home and going back to college, and so lack the time, energy, and motivation to do things with her. Meanwhile, she's struggling to earn a living and has told me she's been cripplingly lonely without me, her family, or others to keep her company. Her living situation has worsened drastically in a short period of time, too; moving between states and living on a shoe-string budget.
To make matters worse, I realize that the love I had hoped would grow as we date is simply not there. In fact, I'm coming to see her more as a sister than as a partner. We've already known each other for so long as friends that I'm finding it hard to see her as anything but. Moreover, she still seems very reluctant toward sexual gestures, contrary to what she expressed. Again, I have no problem with that, but I suspect that she pushed herself to say things she didn't mean just to be closer and to be able to call me her boyfriend. I don't think she did this intentionally (if at all), but it makes me uncomfortable anyway. Our age gap is only a year and a half, but it feels like we're worlds apart in terms of wants and needs. Simply put, I'm starting to think she's too immature for me.
I also realize that the longer I lead her on, the more damage I'm doing by effectively lying. Ideally, I should break things off as soon as possible.
But, and this is why I'm posting here, how could I leave her at such a dire point in her life? I feel obliged to her wellbeing not just as her boyfriend, but also as the friend I've known her as for much longer. Abandoning her at a time like this would devastate her to an extent I don't think she could weather. What do I do?