Can I sell my premium Minecraft account?

Of course - this isn't an MMORPG, there's nothing really tied to your account (other than your avatar), so there's no reason to prevent people selling accounts..

However, for only $13, most people would rather choose their own username, so good luck to you finding a buyer.

Technically, if you read the terms of use for Minecraft, doing this is illegal. Heck, redistributing anyone's copyrighted property for your own purposes is illegal. According to this line in the EULA, it is illegal.

This also means you cannot sell or rent the Game, or make it available for access to other people and you cannot pass on or resell any licence keys.