Maybe. You stated that "she didn't live with me at first". You also say that she moved to Texas, where you also live. Does this mean that she lived in your home in 2009?
Dependent exemptions are allowed for qualifying children and relatives. However there is also a provision that will allow you to take a depedent exemption (even if you are not related) if someone lived in your home, was a member of your household, you provided more than 1/2 of her support for the year and her taxable income was less than her exemption amount ($3650 in 2009).
Find a competent tax preparer. Tell them to enter your friend into their software as a qualifying relative and to complete the depedent support worksheet.