I have an 18 year old daughter.. If she is filing her own taxes, do I have to claim her as a dependent and pay taxes on her income???

Provided she was 18 on Dec 31 2018, and is not mentally or physically disabled, she is not a dependant and you do not include her income in your tax return.

She must file her own 2018, including any claims she has for credits such as Tuition.