I went to the Outlands once I hit lvl 58. Actually, I have had hard time finding quests.

I've done 95% quests in peninsula and 90% in Zangarmarsh, even some very weird gathering quests. And even then I had to grind 70k exp to hit 62 to be able to get last quests in Zangarmarsh and Terokkar Forest. Pretty lame. But on other hand, I have done whole winterspring/plaguelands/silithus and had to grind Tyrs Hand till 58 to go to outlands so I basically have no idea how to quest 58-60.