Shattrath City and the surrounding regions also have a handful of new quests that will probably be less crowded as everyone flocks to the new zone. Daniel Whitcomb covered a few of these awhile ago in detail, but here's who you want to be looking for: Inside Shattrath, you will find Emissary Mordin(for herbalists, miners and skinners), Lord Torvos, and Harbinger Haronem.
Just outside of Shattrath, master anglers can talk to Old Man Barlo for some fun Fishing quests, and there's also a new quest for PvPers in Nagrand. Garadar and Telaar both receive a daily quest for slaughtering the opposition at Halaa. A similar quest can be found in your faction's respective towns in Terokkar for the Spirit Towers.
So don't worry, even the potential soul-searing lag of Quel'Danas won't ruin your enjoyment of patch 2.4! There's plenty of new stuff to do even outside of that zone.