grabref.js

const jsdom = require("jsdom");
const { JSDOM } = jsdom;

var html = process.argv[2];

var dom = new JSDOM(html);
var ary = dom.window.document.getElementsByTagName("a");
if(ary.length >= 1)
  console.log(ary[0].getAttribute("href"));

qute-goto-selected.sh

#!/usr/bin/env bash
href=$(node /path/to/grabhref.js "$QUTE_SELECTED_HTML")
echo $href
echo "jseval window.location.href = '$href'" >> "$QUTE_FIFO"