I am a GA employer and my employee just move to South Carolina. She can work remotely for me. How do I set up her tax withholdings? Do I pay employer taxes in both states

Yes. Your employee can work for you in another state. You will have to withhold South Carolina income tax.

 

South Carolina says: "Wages are taxed in the state in which they are earned unless the employee is working in a state that does not withhold state income tax. If the employee is working in South Carolina, regardless of where he/she is a resident, the income earned in South Carolina is taxed by South Carolina."

 

South Carolina Withholding Tax

 

You don't have to withhold Georgia tax. Your employee does not have to pay GA tax if they live and work in SC.

@ErnieS0  Thank you for your quick response Ernie! Much appreciated!

@ErnieS0 @Would you happen to know the answer to this question. I made over $250K in sales for my S Corp LLC business last year. But, my assets are below $250K. 
Do I need to include schedules L-M. I have researched it and I get confused.

Yes, you have to complete the balance sheet part of 1120-S. The question refers to sales or assets being over $250,000. If your sales are over $250,000, you need complete it. 

@ErnieS0 What about the SUI? Would that be SC as well?

Yes. SUI would be South Carolina as well.