Currently starting pets (for hearthlings with trait “Animal Companion”) stay at the point where they were spawned. This leads to them possibly being killed -> their owners will be very very sad.
To avoid this I suggest such pets to follow their owners from time to time (especially right after a new hearthling is spawned, since new hearthlings are always spawned at some distance from your town).
A possible problem I see is that pets can follow our military guys on patrol and get killed… But is it really an issue? Or a feature?