Can I file as head of household?

I purchased a home in June of 2009 (under my name only). My girlfriend and I have a 2 year old son and we live together (not married obviously). We both work, but she only works part-time and I am able to pay for more than half of the living expenses. If she claims our son as a dependent, can I still file as HoH? I have tried doing some reading, but cannot seem to fully grasp the rules. Was hoping that someone in a similar situation can chime in. Thanks in advance