My girlfriend received her benefits starting jan 07 back dated to may 06. So she was considered disabled for the entire year. During which she was living with me most of the time and I provided more than half of her living expenses. Can I claim her as a dependent and take head of house hold as well?

Here are the requirements:
1. The person cannot be qualifying child of anyone else.

2. The person must live with you all year as a member of your household (and your relationship must not violate local law).

3. The person's gross income for the year must be less than $3,400.

4. You must provide more than half of the person's total support for the year. (So make sure that you had spent on her more than what she received as benefits and her other income.)

Yes

She received around 13k in SSDI income and I know that I spent more than that in supporting her for the year. So does that disqualify her for the 3rd one?

SSDI is not counted as income but you must provide support of more than 13K. So you must have enough income.
Also your state is not one of these states: North Carolina, Mississippi, Virginia, West Virginia, Florida, Idaho and Michigan.

Ryan:

Also make sure that she does not receive any STATE assistance, as the state assistance has to be factored in as well.

Otherwise, claim her.

Of course, for 2008, if you MARRIED her, all of this discussion would be moot, and she could file JOINTLY with you.