It's a minor inconvenience, but it would be nice to have my previously equipped pet persist between sessions. Either retaining the last equipped pet (just like my clothing and weapons loadout), or by allowing me to pick a 'default' pet and pet clothing options to become active whenever I join a new session.

If the issue is 'where does the pet spawn upon joining the server' (since they typically are 'held' when equipping them), I would vouch to have them start 'pinned' to one of the open drop-slots on the ship that's free.