At the time window is loaded the body isn’t still loaded therefore you should correct your code in the following manner:
<script type="text/javascript">
window.onload = function(){
window.document.body.onload = doThis; // note removed parentheses
};
function doThis() {
if (document.getElementById("myParagraph")) {
alert("It worked!");
} else {
alert("It failed!");
}
}
</script>
Tested to work in FF/IE/Chrome, although thinking about handling document.onload
too.
As already mentioned, using js-frameworks will be a far better idea.