You can claim your girlfriend as your dependent if she lived with your for the entire 2016 and you provided more than half of her total support. Her gross income must be less than $4050 for the year - she meets this test since her income is $800.  Her income is not reported on your tax return. 

She must, however, file her own tax return, since her self-employed income is more than $400 for the year.  Since she has no forms, she will report her $800 as cash/checks income.  When your girlfriend does file, be sure that she indicates on her own tax return that she is being claimed by someone else.