Dairy farmers generally don't retail market their own milk. They
sell to a milk coop or consolidator (some "dairies" actually buy milk from other
local dairies, for example, Stewart's Dairy). The entity buying the milk has its own requirements as to the least amount they will pick up. Yes, there are small coops who have in the past picked up or accepted milk from one cow, as long as it passes all the other requirements. This doesn't mean that there is one in your particular area. You may wish to make some phone calls to find out.
As for the breeds, I've never heard of one restricting the breeds. Milk buying depending upon the quality of the milk, taking into factors such as protein and butterfat content. Some small dairies will have several different breeds in order to try to produce their preferred protein, butterfat, and poundage goals.
