While some might argue that 1 letter domain names exist, Micro Domains defines a domain name as the entire URL including the extension to the right of the "dot". This means that the following domain name is actually 3 letters long, not 1 letter.
Since the shortest possible TLD is 2 letters (like .co and .us), that means the shortest possible fully qualified domain name is 3 letters long. There are currently just 26 three-letter domain names available for registration, and they are quite expensive.
Micro Domains considers a domain name short if it has 5 letters or less. Currently, there are 195,506 short domains names available for registration which start at just a few dollars.