I've read Can I add a standard receptacle on a GFCI circuit and have a similar situation in that I need to add a receptacle to an existing GFCI circuit, but when I pulled the existing GFCI plug from the wall, it looks substantially different than the version described there.
What I have looks like this, with connections on both sides:

I suspect they're chained to a receptacle at the second vanity in this bathroom, but unfortunately it's across the room from where I need the new outlet to be (which is right underneath this one). What's the correct way to make this happen, short of calling in an electrician?
Thanks!