But don't worry too much just yet. There is conflicting information in Blizzard's official Faction Change FAQ:
What will happen to the character's non-combat pets when I change its faction?
Non-combat pets will not be affected by this process and will be available once the character's faction change completes. This even includes faction-specific non-combat pets.
So which is correct?
Honestly we're not sure. But we hope Blizzard will clarify it soon. It may affect whether the transfer is worthwhile for several pet collectors. We'll keep you posted.