adding an GFCI outlet off an existing outlet. 120v two wire with ground
The existing outlet probably has another set of screw contacts specifically for a downstream outlet. If it does not, you should replace it with a newer outlet.

http://www.how-to-wire-it.com/images/296xNx2-outlets-in-series.jpg.pagespeed.ic.vFuUvogAxu.jpg

Make sure you hook up the ground to the new GFCI.  

I'm gonna guess that if you ask the manufacturer or an electrician they will suggest or require that you add a new run from your panel with a dedicated breaker.  But as a DIY'er, I would run it as you said from an existing run.