Ok, so I asked my DM this question: "Suppose a dryad got the ability to teleport, could be an item, could be innate, how doesn't matter. Now, can she take her tree with her?"

He thought about it for a minute, then replied, "Since she is the tree, one could argue that she could take it with her. One could also argue that she MUST take it with her."

So I thought I'd throw it open to the playground for a bit. My DM has no firm opinion, so surely there are those in this forum who'd like to analyze this, as this is almost certainly going to set the precedent for a LOT of spells used in our campaign, as due to player shenanigans, there are going to be thousands of spell-using dryads about. So, should they be able to cast the spell Fly and you see this humongous oak soaring through the air?

Gaseous Form? She and her tree turn to mist, a mist that works its way into every crack of a building, then reforms?

Show me your ideas. They could be a powerful influence on my DM's opinion.