Make a reservation for an overnight stay at the mountain hut.
July is perfect for a multi-day hike, but mountain weather can change quickly. Take a look at the weather forecasts a couple days in advance.
In summertime (June to September), you can start the hike as late as lunchtime, because sunset isn't too early. On the first day, the hike takes about 2-4 hours up to the mountain hut.
I wouldn't recommend doing the hike from November through March because of snow.