How do I file as Head of Household with a non-relative dependent?

My GF of 6 years collects disability, has no other income (so below the 4,400 GI requirement.  I pay for essentially all our living expenses.  It allows me to claim her as a dependent, why can't I file as Head of Household?  If through the exceptions she is a qualified dependent, and I pay for essentially everything, I should qualify shouldn't I?