I filed a federal extension and it was accepted. Does that automatically get me an extension on my state return for GA or do I need to file that separately

[DMarkM1]

No, you do not need to request a GA extension separately.  GA accepts the federal extension.  

However, if you expect to owe a GA tax you should visit the GA state interview and click through to the "Other situations/forms" page and file the extension and get an estimated tax to be paid along with payment options.  Here is the GA DOR reference.