When do we eat moon cakes?
The answer is: any time you like. Typically when Dragon Boat Festival is over, you will start to see advertisement everywhere about mooncake, which means you can start to buy moon cakes!
Eat it any time you like. You don't have to save it till festival night. But after the Mid autumn festival, everybody is tired of it and no one would want to eat it.
Installment for moon-cakes
As I said, if you love to eat mooncakes or you have lots and lots of relatives, you will need a lot of moon cakes. I remember when I was a kid, some major mooncake bakers have already launched the moon-cake installment plan. Basically, you choose how many boxes you want and you start to pay the baker one year in advance month-by-month. The baker will also throw in goodies like Chinese preserved meat sausages.
Source : http://www.hkfastfacts.com/Chinese%20Festivals/mid-autumn-festival-moon-cakes.htm