You can try this:
var a = document.createElement('a');
var linkText = document.createTextNode("Text for your student");
a.appendChild(linkText);
a.title = "Text for your student";
a.href = "your url";
document.body.appendChild(a);
Here is how you can append your div with your new element:
function getFavourite()
{
var name = document.createElement('a');
var linkText = document.createTextNode("Student 1, ");
name.appendChild(linkText);
name.title = "Student 1, ";
name.href = "your url for your student";
$("#output").append(name);
saveFavourites();
loadFavourites();
}