How far in advance can shortbread be made, and should it be frozen (say for a month)

I agree with boulangere. I have successfully frozen shortbread for several months (lost in freezer). The key is good wrapping as boulangere says, for air is the enemy in the freezer.

Shortbread is very high in fat and low in moisture, so it is likely an excellent candidate for being frozen. I'd suggest double-wrapping it in a good quality plastic wrap, not just a zip lock bag.