gistfile1.js

function getKeys(obj) {
  all = {};
  function get(obj) {
    var keys = Object.keys(obj);
    for (var i = 0, l= keys.length; i < l; i++) {
      var key = keys[i];
      all[key] = true;
      var value = obj[key];
      if (value instanceof Object) get(value);
    }
  }
  get(obj);
  return Object.keys(all);
}

Keep in mind, this needs an implementation of Object.keys which can be polyfilled with:

Object.keys = function (obj) {
  var keys = [];
  for (var key in obj) {
    if (obj.hasOwnProperty(key)) keys.push(key);
  }
  return keys;
};

Also there is no protection against cycles in the object. That could added at a performance and memory use cost if desired.