How to query for a week using key => value WP_Query argument notation?

There isn’t a week query variable, but there is w: http://codex.wordpress.org/Class_Reference/WP_Query#Time_Parameters

w (int) – Week of the year (from 0 to 53). Uses the MySQL WEEK command. The mode is dependent on the “start_of_week” option.

Your args should look like this:

$args = array('category_name' => 'whats-happening', 'year' => 2012, 'w' => 46 ,'paged' => $paged);