Slight correction: the proposal was for a "Ministry of Sex", not a "Ministry of Unsatisfied Women" – but ultimately, yes, that was the target of the proposed ministry, yes, this brawl happened, and yes, you can watch the video here (brawl starts at 46:10; I timestamped 41:30 for the start of Karapetyan's speech).
Edit: Not speaking Armenian, I can't actually tell if this was the insult that was traded. I don't see any reference to it anywhere, and I even tried looking at this thread on Reddit's /r/armenia to see it mentioned nowhere either.
Edit 2: Top comment in that thread, by the way, is:
41:30 During Taron Chakhoyan's speech Narek [Karapetyan] made remarks, Chakhoyan responded to him, then Narek stepped up, a fake performative brawl happens, everyone settles down and someone not in the frame says (or does?) something (audio muted), and everyone runs towards that direction and a real brawl begins. Can't tell who's who anymore, it's hard to tell.