I think you are asking about how to design whilst using a retina display, rather than asking how to design for retina displays. You don't need to change anything about the dimensions you choose.
If you create a 120px header on your retina display, it will appear as 120px high on a non-retina display - you don't need to change your behaviour because you're using a retina display.
Mac OS X scales everything you see behind the scenes, so when you create a 100x100px image in photoshop it is actually occupying 200x200 pixels on your display. If you double the pixels yourself, you'd have a 200x200px image displaying at 400x400px - which is not your goal.
If you want some proof of this, try creating a 100x100 image in photoshop, then use CtrlShiftCmd4 to take a screenshot of it. Now CtrlV in a new layer, the screen shot will be twice the dimensions of the image.
If you want to design for retina displays, any advice given regarding dimensions has nothing to do with what sort of display you are using.
Just to try and clarify my point:
I'm wondering if I should be doubling up on everything in Photoshop to get what it would look like [...] on a non-retina display?
To produce something that looks like it would on a non-retina, you produce exactly what you did before.
To produce a double resolution graphic, that only retinas can fully display (although of course can be scaled by a browser on a non-retina), you would indeed double the resolution.
But my point is that you would have to do that even if you weren't using a retina display right now.