TheWoWDBJust in case this is relevant for anyone, yes, you can store your pets here.
I might've deliberately gone out of my way to hoard any neat looking pets I could find from here before proceeding since there's no known way to return to Exile's Reach yet.
Humanoid
Mithdran Dawntracker
Stable Master
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Details
This roster comes from the current game client's data files, so it is not a complete list of every NPC in the game - older world NPCs that are no longer in the modern client are absent.
Community notes from Wowhead · 1 comment
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Level and Map Tracking
The game data tunes Mithdran Dawntracker for levels 1 to 10, Classic content.