Yesterday, the Warlords of Draenor Patch 6.0.2 released, and once you logged in the first time (with a level 90 character), a quest starts automatically and leads you to the blasted lands. All the quests from there do get you armor, but I don't get experience, theres not even an amount of experience displayed on the quest itself, is this a bug or am I doing something wrong?
No, this is not a bug.
You are actually not playing the expansion itself yet, but its prepatch. Yes, general changes like the item squish, draenor itself and talent changes etc. are already patched in, but the level cap stays 90 until WoD releases (13th of November I think). You currently do the pre-quests for Draenor, these probably intend to gear you up, make you ready for Draenor itself.