I am one of the straighties but I do understand what you're going through.
Jacko is right, that you can't possibly be responsible for your girlfriend's happiness, but I get that as a carer it often feels like this is your role. What sorts of things does your girlfriend find even just a little bit of joy in? Is she willing to do any of these things even when you aren't with her? Is she working at the moment? Are you also working?
Is your girlfriend getting any professional support with her problems? Is she taking any medication to help with her low mood? Does she have other family/friends that she can also rely on for support?
Do the two of you communicate quite openly about her concerns, and how you are BOTH feeling? I do think that as a carer you can easily get caught up in supporting your partner, and you start to feel like it would be too much for her to hear about how you're coping. It is, however really important that the communication go both ways.
Have you spoken with your GP about your worries around your carer role? Carers need support too. There are some options available to you. Obviously seeing a GP is one of them. There's also the carer's Australia website. There are a number of support groups available to carers. One thing that I arranged for my partner was for him to have 24hr access to my Psychiatrist. He was also invited to some of the sessions. Through the hospital that I'd been admitted to, they offer carer information evenings, this might also be something to research.
I do hope that this has been helpful.