I just want to make sure I get this straight. My girlfriend and I have a four year old daughter and we are using turbo tax to do our taxes this year. What I want to know is can both her and I claim our child on both of our separate tax forms and if not which one of us can claim her as a dependent. And who could claim head of household or can both of us claim head of household.

Only one of you can claim her. IF you do your own taxes figure them out with her on yours and then on hers and see which one works best.
If you have someone doing your taxes they should be able to tell you right away which is best.

If you aren't filing a joint tax return then only one of you can claim her. Whoever has physical custody is the one. That person files as head of household, the other files as single.

Only one of you can claim her, and the one that does can claim "head of household"

You should figure the taxes both ways and find out which way works out best.

Also if you want that married tax rate, I do wedding specials in Atlanta on Saturdays.