Note to self : Make sure to read the answer carefully, and follow the link. (maybe I saw the mention of yeast in the question, and didn't see he had said he knew how to deal with yeast).
Chemical reactions will slow at colder temperatures, but I have no idea by how much, or if it even applies in this case. The chemical reaction would've happened quickly, assuming the baking powder was mixed in well and I suspect it's that you need the dough to relax some ... which would be inhibited by the fridge, but if that's the case, you'd have to let the dough warm back up again (which might be 30 min or so, defeating much of the point of this)
Although they do call for putting the dough in the fridge for a few minutes if it's too sticky, that is significantly different from letting it get cold all the way through.
I wouldn't try to leave it to rest out of the fridge, because the air will slowly escape, deflating the dough. This is less a problem with double-acting baking powder, as it'll release more gas when it's heated.
If the situation is that you have some time now, but not enough, and you'll have more time later -- then I'd mix up the dry ingredients now. You could also cook the butter/sugar mix, but you'd want to put that back into the fridge and re-heat it later (maybe a low microwave?). When ready, mix the eggs into the dry stuff and add the butter/sugar blend.
(and in reading the recipe -- I don't know if "Serves 1 - 50 Cookies" means that one person will eat all 50 cookies, or that you could make one large cookie or 50 small ones)
Original (bad) answer follows:
I frequently let things rise in the fridge overnight or while I'm at work (or both), when the recipes call for leaving it 'until doubled'.
I typically put it in a container about 3 to 4 times larger than the volume of dough, loosely lidded, with something heavy on top of it (in case it tries to rise so much it comes out of the container).
When you take it out of the fridge, you may need to let it warm back up a little bit, as it can cause things to be a little bit stiffer than it would have been at room temperature.
I would not leave it out at room temperature, as it would ferment much more than called for in the recipe.