The usual time period for taking on Triglav is during summer or fall. Experienced mountaineers may also do this in winter conditions. For those, the hut on Kredarica (Triglavski dom na Kredarici - 2515 m), while officially closed, provides basic lodging. You get a blanket, bed in unheated quarters and that's about it. The service is provided by a group of meteorologists that occupy the Kredarica station throughout the year.
The huts around Triglav usually open officially in June/July, depending on conditions. For Triglavski dom na Kredarici specifically, its official website claims that they will start accepting reservations for 2022 on June 27th in 2022 (at time of writing).
The Alpine association of Slovenia website provides reliable information on mountain/hiking trails across Slovenia. You can find information about Slovenian huts on their sub-site here. The sub-site for Triglavski dom na Kredarici may be found here - Slovenian version provides more information (use translate).
Note: the route description you stated in your question is rather sketchy (obviously written by an experienced mountaineer in a hurry). At the very least, a map of the route would be expected. Perhaps check this site for more detailed route information (there are several marked routes possible from Krma valley to Triglav). Again, the Slovenian version of the site contains more information, including maps and comments.