Wizard101 is a story driven game. You must complete one chapter before you move on to the next.
Just as you had to complete your required quests in Wizard City to gain access to Krokotopia at the Spiral door, so much you complete Krokotopia required quests to unlock Marleybone, and so much you complete Marleybone to open access to MooShu.
And yes, before you can enter Dragonspyre, you need to complete your required assignments in MooShu. You must complete Dragonspyre to enter Celestia, and complete Celestia to enter Zafaria.
Grizzleheim must be completed before you can enter Wintertusk, and Wysteria, for now, is a stand-alone zone.