I agree with Jadzea -- I'm not sure you're THAT committed to your girlfriend that you want marriage right now.
The group home is offering you complete care and that is what you WANT. The fact that you and your girlfriend would be scratching for pennies would cause all kinds of stress and could even mean that you wouldn't be able to get your insulin. If you can't handle money, then you wouldn't have enough for your medications. Then where would you be? You two would be fighting all the time, and that's going to break down a marriage quickly.
I vote for the group home. While she may be hurt, it's better than getting married and then quickly getting divorced. I'm afraid that's what would happen, and that would hurt her even more. Let her go to find someone else. You can still be friends.

God bless and please take care. Hugs, Lee