You can create a temporary parent node, and get the innerHTML content of it:
var el = document.createElement("p");
el.appendChild(document.createTextNode("Test"));
var tmp = document.createElement("div");
tmp.appendChild(el);
console.log(tmp.innerHTML); // <p>Test</p>
EDIT:
Please see answer below about outerHTML. el.outerHTML should be all that is needed.