Mueller Hut Route is one of the most beautiful walks I have done. As the hut was booked out, we camped at White Horse Hill Campsite (which is at the base of the track) and went up to the hut and back within a day. What makes this route awesome is the proximity to the campsite, combined with short distance, large vertical gain and mild track conditions in good weather. It feels like climbing to the top of the world—no mountaineering experience needed!
Check the weather! It seemed pretty doable on the sunny Saturday we attempted it, but the very next day the weather packed in; crampons were necessary on the route and we wouldn’t have been able to do it in such conditions.