According to the documentation of that date picker, that should work. Are you sure that nothing is modifying $sDate and $eDate prior to your query. What you may want to do is this. Change the action on your form to post to another file and in that file just put this.
<?
echo "SELECT * FROM tsttbills where DATE_FORMAT(billDate, '%e-%m-%Y') >= '" . $_POST['sDate'] . "' and DATE_FORMAT(billDate, '%e-%m-%Y') <= '" . $_POST['eDate'] . "'";
?>
This way we can eliminate the date picker as the issue.