First of all, the variable script contains the sequence </script> which you can not make it appears as it is in your code, because browser will assume(and it must) that it is <script> tag close.
for example if your script code contains syntax error, which is a string variable that has no close " it will looks like
<script>var bad = "abcd ;</script>
to solve this you can break the </script> string like "</scr" + "ipt>" or you could escape it: "<\/script>"
so:
var script = '<script type="text/javascript" src="http://code.jquery.com/jquery-1.9.1.min.js"><\/script>';
document.getElementsByTagName('head')[0].appendChild(script);
Second thing is that appendChild() function accept a Node element and not a string
so:
var script = document.createElement("script");
script.src = "http://code.jquery.com/jquery-1.9.1.min.js";
document.getElementsByTagName("head")[0].appendChild(script);
Anyway, I prefer to use a module and JavaScript loader like RequireJS.