I just checked random weekdays in July and pulled up a ticket for 628,000W H class ticket. It's not their cheapest Q sale fare. If you are finding Q fare class, that will be their best sale deal. Personally, if you like the price, I'd say buy it now. Korean Air is very old school with their sales. They have them for an extended period, but once they're gone, they're gone. They don't like randomly release a sale two months before hand. Always advance purchase before 60 days.

I flew to ULN once, but it was during Lunar New Year, so the flights were 100% full in both directions. Not sure about normal loads in July, but you'd be surprised. As many Mongolians do have to make it other places, they often connect through KE so I'd expect flights to be pretty full.