Can i claim our daughter that we supported for 9 of the 12 months in 2017? Or because she started working in October, did we lose the benefit?

Yes, you can claim your daughter if you meet the Qualifying Child rules below. She can also file her own tax return and receive a refund of the taxes withheld or balance owed (if she's required to file). However, she must indicate on this tax return that she can be claimed as a dependent on someone else's return.

To be a Qualifying Child -

1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.

2. The child must be (a) under age 19 at the end of the year, (b) under age 24 at the end of the year and a full-time student or (c) any age and permanently and totally disabled.

3. The child must have lived with you for more than half of the year. Temporary absences while away at college are considered living with you.

4. The child must not have provided more than half of his or her own support for the year.

5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child. 

6. The child must be a U.S. citizen or U.S., Canada or Mexico resident for some portion of the year.

7. The child must be younger than you unless disabled.

Here's a link with information about Filing Requirements: https://ttlc.intuit.com/questions/1901490-do-i-need-to-file-a-federal-return-this-year?jump_to=answe...