If you have php between the javascript and MySQL it is easy to convert the string from the javascript: '(DD/MM/YY)' to a 'YYMMDD' format accepted in a DateTime field in MySQL using
$dateArray = explode('/', substr($javaDate, 1, -1));
$mySqlDate = $dateArray[2].$dateArray[1].$dateArray[0];
$javaDate is the string from the javascript, substr to get rid of the parenthesises and explode to extract the different date fields into an array. The resulting $mySqlDate can then be inserted into the database.