Re: Building a stone post
It depends on where you live. The reason is that you need to have a footing that goes below the frost depth. You should be able to find the average or deepest frost line for your area from you local building code department, or google on the internet, maybe.
You can probably use a post hole digger to make a hole to the proper depth. Local building codes would specify the minimum diameter but the building codes may not apply due to the height of the structure and that it is not a habitable structure. Then cut the square slab at what ever depth you want, it can be just a few inches under the soil if you want, that will save on stone that will be underground, but there probably should be at least one stone depth underground so that it will look more natural.
You could also confine your mortar to the inner part of the column so that there is no mortar in the outer 3-4 inches if you like the dry stack look, just make the mortar a little richer in cement to give it more strength.
But your way will work also as long as the frost line is less than 18-24" deep in your area.