AFAIK it might not be available in JS. You might need to custom implement.
Found a solution to it. All the properties of the page gets stored in an json object which can be accessed by appending .1.json to the page url. If http://localhost:4502/content/en.html is your page, then http://localhost:4502/content/en.1.json gives your page properties. Hence, we can extract the required property(cq:template) from the object using getJSON() method.