Nothing against your idea but if this is a plot device character that exists to progresss the story for the characters then it really doesn't need rules.
It can move beyond tree range because it has to for the plot. Fluffy reasoning it's a rare unbound dryad gifted the ability to travel far to further X deities agenda.
Unless you have a dryad in the group, rules are not required.
But if you would prefer to keep within the rules for your dryad instead of home brewing something why not take this approach
The dryad is a regular dryad bound to a tree. But the tree gets teleported by someone/something and the dryad goes along with it .
After a while the group may recognise the tree before they see the same dryad which would be a cool way to let them know they were safe even in an area which just before seemed very dangerous.