I have gone from level 1 to level 15 (1 quest a day) on just pandaren tamers and elements. I don't do this with the fabled so I don't know how safe they are, but I know several would be suicide.
Out of all 11 tamer/elemental spots only Seeker Zusshi has given me problem. It can be done but there is a Basilisk with in range if you are to close. He wanders around a small mound, if he is on the far side you can interact with Zusshi but if he comes around before the battle starts he will agro. I still die but the release spot is fairly close so not a far run back. The danger comes when the battle finishes it is tough to time when he is in the right spot. Standing at the waters edge is safe, but 3 steps or so forward is deadly, which is about where you end up after the battle finishes.
I have 2 accounts so I was able to fly my alts out to each one with no trouble.
In the spots where there is no handy mailbox I have flown my engineer out and dropped a mail box to mail the stones back to my main if it is a stone I couldn't use right away. I currently have all pets rarified so at this point all stones are being stored for now.
The bonus of doing this is that one exp pet treat can last for a couple weeks if you log in do the battle then log as soon as you are finished. I have my all my pet teams set up and ready to go, I really like Rematch for the pet queue to automatically switch in the new leveling pet when one gets maxed. Can usually get on get the battle done and log out in under 4 minutes. Most teams don't lose, but there are a few battles that you need to be careful how much HP your leveling pets have in order for it to survive. Any of the battles that have back row damage makes it tough to have a level 1 survive. Wastwalker Shu and Farmer Nishi come to mind.