The answer marked is perfect but for one scenario, where in the dd and mm are actually single digits. the following regex is perfect in this case:
function validateDate(testdate) {
var date_regex = /^(0?[1-9]|1[0-2])\/(0?[1-9]|1\d|2\d|3[01])\/(19|20)\d{2}$/ ;
return date_regex.test(testdate);
}