Changing charset in $.ajax?

Question

I need to send data to the server using the character set Big-5, however the browser seems to only encode the data in UTF-8. If I were to make a form, then it can be achieveable with the following attribute:

<form accept-charset="Big5">

However, I want to send the data through XHR. Some answers suggest that contentType can let me change it. But according to jQuery's documentation, the encoding cannot be overridden: (at least this is true in Chrome.)

The W3C XMLHttpRequest specification dictates that the charset is always UTF-8; specifying another charset will not force the browser to change the encoding.

$.ajax({
    url: "dummy url",
    type: "GET",
    data: {
        q: "Test"
    },
    contentType: "application/x-www-form-urlencoded;charset=Big5"
}, function(){});
//This won't work.

Is there any way to get around it?