When I was younger (2003) I rented a movie which I believe to be an anime, though I do believe it was older.
The details I remember:
(Space Pirates aren't actually in space, they are just named that for convenience, they just fly about in airships)
In the beginning of the movie, there was a boy, who happened to come across, or see a girl falling from the sky, but she never hit the ground, she was floating. (They were young, by appearance, I would say between the ages of 7 and 14)
I remember a scene rather vividly, where the girl (from above) was climbing on the outside of an airship, trying to escape what I shall call Space Pirates as to not let them gain an amulet (not sure on whether it was an amulet or something else entirely, I just know she had it, the space pirates wanted it).
I remember the two of them (Boy and girl, from first point), found their way, somehow onto an island which had a giant tree on it, with a lot of robots which had the ability to fly, it was an old looking place with moss and other overgrowth about.
The girls amulet, (or other item), had some sort of ability here, and was special to the island. I'm note sure, though it may have been that the amulet woke the robots.