Assuming by "redirect" you mean "navigate to"... how about this?
function doSearch (){
var win = window.top.getBrowser();
var tab = win.selectedBrowser;
tab.contentWindow.location.href = "http://google.com";
}
That should be OK provided your XUL is an overlay to the ChromeWindow hosting the TabBrowser in question.
See MDN: Tabbed Browser for some other scenarios.