Alternative to jquery $(document).ready(handler) when using javascript page transitions

In a simple plugin for my wordpress, I wrote code that sets up click events as follows:

$(document).ready(function() {
    $("#myButton").click(function() {
        //do stuff
    });
});

This code works as expected when I load the relevant page directly. However, the way users are expected to access the page is through a link in the theme header. I am not really sure how page transitions in the theme work, but the end effect is that whenever a link is clicked, some animation happens, the page fades out, and the new page fades in. The problem is that $(document).ready() does not fire when the new page fades in, so the click handlers do not function.

How can I change the code so that the click handlers are registered at the time the new page fades in?

If it's necessary to see how the theme works, I am using the Bridge Theme. A demo version of the theme is available here.