Not all the query_posts args support the comparison operator (only meta parameters do if i remember correctly), so you have to look at the ones that exist for exclusions, in this case tag__not_in .. which excepts the tag ID..
If the tag doug has an ID of 5, then you would use something like..
<?php
$args = array(
'showposts' => $mytheme['carouseln'],
'cat' => 2,
'tag__not_in' => array(5), // Assuming 5 is the ID for the tag doug
//'tag' => 'doug',
'order' => 'asc'
);
// NOTE: Orderby sets the database field to sort the results by - Order sets the direction, ASC or DESC
$carousel = new WP_query();
$carousel->query( $args );
?>
It's the same deal as what you're doing with the category, using the ID instead of the name..
Further reading: http://codex.wordpress.org/Template_Tags/query_posts#Tag_Parameters