There is no such thing as a Mini Siberian Husky however there is a breed that looks like a Mini Siberian Husky. This breed is called the Alaskan Klee Kai. They have been around since the 70s and I'm not sure there are too many breeders of this breed. People often refer to them as Mini Huskies. So it may be difficult to find one.
The UKC does recognize them as a breed but I don't think the AKC does. My breed of choice is not recognized by the AKC either, the American Pit Bull Terrier, but they are recognized by the UKC. A lot of people feel the AKC is the know all end all of dog registries. lol Just because a breed isn't recognized by the akc doesn't mean they aren't a real breed. The AKC only acknowledges a handful of breeds.
Here is some info on the Alaskan Klee Kai
http://en.wikipedia.org/wiki/Alaskan_Klee_Kai
Here is the UKC breed info on them
http://www.ukcdogs.com/WebSite.nsf/Breeds/AlaskanKleeKaiRevisedJuly12009
Make sure you go through a reputable breeder. Go to some UKC shows and talk to the owners/handlers of the dogs you like and I'm sure you will find a good breeder. Most good breeders don't advertise online or in the paper. You want to make sure the parents have had proper health testing as well.
Good Luck
More Info on the breed:
Appearance:
They come in three sizes based on their height:
Toy size Alaskan Klee Kai are up to and including 13 inches.
Miniature Alaskan Klee Kai are over 13 inches high and up to 15 inches high.
Standard Alaskan Klee Kai are over 15 inches high and up to 17 inches high.
Serious Fault - Any Alaskan Klee Kai over 17 inches and up to 17½ inches.
Eliminating Fault* - Any Alaskan Klee Kai over 17½ inches
Alaskan Klee Kai come in four main color varieties. Black and White, which can appear with stark contrasts or with a more dilute diffusion of the colors; Gray and White, which comes in several variations; Red and White, which appears either as a cinnamon or a dark auburn, or shades of white.
Grooming:
As in Siberians and unlike short haired dogs who shed all year long, the Klee Kai blows their coat twice a year. Of course, the size of the dogs limit the amount of fur blown. It is best to groom the dog on a regular basis during this time. Some of the longer haired dogs can become matted if not groomed. Most Klee Kai will assist the loss of hair by rubbing against things such as fences.
Other than this period of blowing coat, the Klee Kai is very self sufficient
Temperment:
The Alaskan Klee Kai is a highly intelligent, curious and active breed. Unlike Siberian Huskies, whom they closely resemble, Alaskan Klee Kai are typically standoffish and cautious around unfamiliar individuals, which causes them to excel as watchdogs. Because of their inherently reserved disposition in the presence of strangers, continual socialization throughout an Alaskan Klee Kai's life is highly encouraged