The tree is a separate living organism. More specifically, a plant. The target line of the spell says, "You and touched objects or other touched willing creatures." There may be some argument over whether the tree counts as an "object" or a "creature". Plants without stat blocks are sometimes treated as objects by the rules, and sometimes they are treated as creatures. Either way, it's possible that the druid could bring the tree along. However, size may be a limiting factor. If it counts as an object, then the dryad has a weight limit based on their max load (Str 10, so 100 lbs). If it counts as a creature, then you may need to decide if the tree counts as large (counts as two medium creatures) or huge (counts as four medium creatures).

Outside of acorn of far travel, there may be other methods for a dryad to move her tree around. Smokey confinement (Complete Mage) might work. A modified bag of holding with some combination of a Ring of Sustenance, Necklace of Adaptation, Decanter of Endless Water, or a Wind Pipe (Stormwrack) could provide the dryad with some mobility.