Unfortunately your "from" dateformat is not the one which is implementation-independent in JavaScript. And all the other formats depends on the implementation, which means even if this format would be understood by most of the implementation I/you can't be sure for example how the DD and MM order would be parsed (I am almost sure it would be local regional settings dependent). So I would recommend to use a 3rd party (or your hand written) date parser to get a Date object out of your input string. One such parser you can find here:
http://www.mattkruse.com/javascript/date/
Because your question is not 100% clear for me, it's possible that you have your date in the format of /Date(number)/ which suggests that you are calling an ASP.Net service from your jQuery code. In this case during the JSON parse you can convert it to a Date object:
data = JSON.parse(data, function (key, value) {
    // parsing MS serialized DateTime strings
    if (key == '[NAME_OF_DATE_PROPERTY_IN_THE_JSON_STRING]') {
        return new Date(parseInt(value.replace("/Date(", "").replace(")/", ""), 10));
        // maybe new Date(parseInt(value.substr(6))) also works and it's simpler
    }
    return value;
});