Pre Legion Scenario and New Dal Quests for Kara/Ulduar on Alts?

Will I have to do all the stuff for Khadgar (go to Ulduar and Karazahn for New Dal Quests) before I can get to Legion content?

I have done it one three so far but doing it ten more times seems rather tedious and boring.

I tried flying to Deadwind on two different alts and Kara wasn't in the air there yet. I also didn't see the portal to New Dal.