A few weeks ago, Blizzard made it clear that the quest tracking feature, which was added with patch 3.3, would not be available in Wrath of the Lich King Classic. A few hours ago, however, WoW Classic Game Producer Aggrend confirmed that this feature can be expected in the course of the expansion.
Hi Everyone,WoW Classic Game Producer Aggrend
Just wanted to pop in and say that we do in fact intend to implement the quest tracking features that were added in patch 3.3 of original Wrath of the Lich King into the Quest Log and Map UI at some point. The interviews linked by the OP were a few months old and our thinking has changed quite a bit on this since then.
This feature isn’t present on the Wrath of the Lich King Classic beta at this time, but this along with several other UI features such as the Calendar and Equipment Manager are still in active development.