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Please refer to the IRS publication 501 - http://www.irs.gov/pub/irs-pdf/p501.pdf - please be aware that this publication for 2006 - updated version for 2007 is not released yet. Please review pages 9-14 that related to your question.
There are five tests that must be met for a child to be your qualifying child. The five tests are: Relationship, - For your situation - an eligible foster child is an individual who is placed with you by an authorized placement agency or by judgment, decree, or other order of any court of competent jurisdiction.Age,Residency, - To meet this test, your child must have lived with you for more than half of the year.Support, - To meet this test, the child cannot have provided more than half of his or her own support for the year.
and Special test for qualifying child of more than one person.
Based on information provided - either - you or your girlfriend are eligible to claim the child and either may be a head of household.
Yes, you are correct - according to publication 501 - http://www.irs.gov/pub/irs-pdf/p501.pdf page 7
you may be a head of household in you have a quilified child whether or not you can claim an exemption for the person. So you may be a HOH even if you are not claiming the child as a dependent.