These are some of the areas or maps to get some pets while questing.
Kryta
Queensdale
Kessex Hills
Gendarran Fields
Harathi Hinterlands
Bloodtide Coast
Maguuma Jungle
Caledon Forest
Metrica Province
Brisban Widlands
Mount Maelstrom
The Grove
Shiverpeak Mountains
Hoelbrak
Dredgehaunt Cliffs
Timberline Falls
Ascalon
Fireheart Rise
Plains of Ashford