This data is stored in the meta-table qa_userpoints. The qposts columns has the number of questions they have asked. So a query like this would do it:
$result = qa_db_query_sub('SELECT qposts FROM ^userpoints WHERE userid=#', $userid);
$qposts = qa_db_read_one_value($result, true);
$userid there might be $post['raw']['userid'] instead, if the query was run in one of the theme functions.