How to denote the standard deviation with siunitx?

The code you are looking for is on page 43 of the siunitx manual (as of 2011/10/14):

When a number has multiple parts (such as a separate uncertainty) then the unit must apply to all parts of the number. How this is shown is controlled using the multi-part-units options. The standard setting is brackets, which will place the entire numerical part in brackets and use a single unit symbol. Alternative options are repeat (print the unit for each part of the number) and single (print only one unit symbol: mathematically incorrect).

\sisetup{separate-uncertainty}%
\SI{12.3(4)}{\kilo\gram} \\
\SI[multi-part-units = brackets]{12.3(4)}{\kilo\gram} \\
\SI[multi-part-units = repeat]{12.3(4)}{\kilo\gram} \\
\SI[multi-part-units = single]{12.3(4)}{\kilo\gram}