Footing for 12" garden wall
Really for a 12" wall you should only have to dig down enough to make it level and a gravel base under the footing (the gravel will help drainage and spread the weight of the concrete. This would the be considered floating. If you live in an area that freezes the wall will move some. As in outdoor building with floating slabs. But it should not be to much of a problem. If you did wish to prevent movement or your area had building codes for this type of thing then you may has to dig down bellow the winter frost line. About 4 to 5 feet in northern Illinois. This varies depending on were you are.