Enka, we did the tour Ljubelj - Zelenica - summit of Begunjščica - Roblekov dom - return via Roža to Prevala - Bornova pot - Ljubelj about a month ago.
Definitely recommend going up via Zelenica, as you hike the northern slopes of Begunjščica, which means less sun and cooler, and return via the southern slopes to Prevala, thus making a nice loop tour.
I hope it will be useful to you. Good luck.