For 2016, 19 year old earned $9,300, went to college (9 credit hours per term)but not full time, still lives at home. Can we claim her as a dependent?

Yes. You can claim your child as a dependent if she lived with you for more than half the year in 2016 and if she meets the IRS definition of a student. Additionally, there are other requirements that you would need to meet. 

Please refer to page 13 of Pub 501, under the headings, "student defined", "full time student", and  "school defined",  to determine if your child meets the IRS definition of a student.  https://www.irs.gov/pub/irs-pdf/p501.pdf

Additionally, please refer to the chart on page 12 of pub 501 to see if you meet the requirements to claim your child as a qualifying child. Please note that there are requirements listed above the qualifying child and qualifying relative sections, and those requirements must be met as well.  https://www.irs.gov/pub/irs-pdf/p501.pdf.

If she doesnt qualify as your dependent, then she would be the only one who could claim an education benefit.