Sorry you are having issues, please note:
The last place you put your pet or thrall on guard is his new home. That can be anywhere that is not landclaimed by someone else or blocked by the server (city, camp, dungeon, etc.)
The pet first goes into a ‘scouting’ mode and stays where he is for a while. I do not know how long that is.
When the ‘scouting’ period is over, the pet travels to his home (last guard position), but it can take a while. Often they walk. Sometimes they teleport.
On rare occasions, I have logged in more than a day later, and there he was. He finally made it.
It usually takes quite a bit less than that, but please be patient and make certain you remember the last place you put him on guard.