The route you are planning is totally easy - I am actually not sure if you have to take your hands off your pockets for a single time
One exception is at the Koča pri izviru Soče if you decide to go to the source itself - there is a short protected section (this is not the part of the route and not necessary, but recommended).
However, I have some second thoughts about the second and the third day of the hike - the third day basically consists just of a two hours descent and then a long hike along the shores of the lake. If you want to do this, it is fine, but to my taste there are two more interesting options:
1. sleep at the Triglavska jezera hut and next day cross the plateau above Bohinj lake over Planina Pri jezeru and Vogar, then descend to Stara Fužina. Everything easy except for a short protected part on the direct route over Štapce above Triglavska jezera - which can be avoided by using the longer route further south.
2. Maybe even more interesting - instead of going to Triglavska jezera via Velika vrata, you can use the Prehodavci route - in this case, you can either sleep at the Prehodavci hut or continue down the valley to Triglavska jezera. From then on, you can either continue as described at 1 or descend directly from Prehodavci via Za kopico valley - this is a bit more off the beaten track and maybe more difficult to find (though marked), but beautiful. Then on to Vogar and Stara Fužina. This way you actually hit the 2000 metres mark, but it is still an easy hike.
Of course, either way, you can (and will) still have a swim in the Bohinj lake in the end.
Have fun!