My daughter did not work or receive a W-2 for 2019. She has herself and 1 dependant, Does she have to file for 2019?

If she had no income and did not get health coverage through the marketplace she doesn’t have to file. 

Who is supporting her if she has no income?  Can she and child be claimed as dependents?

If she has no income of any kind then there is no reason or need to file a tax return, with or without the child.

She doesn't have to file. However someone has to be supporting her and her dependent, so whoever has paid for more than half their support for the year can claim them as dependents.