siriuslydementd im guessing Jack just wants his Doctors attention?

something like that, yes

Does Jack know what he wants?

he has no idea

by his point in the future, it might not even be a human tradition anymore

what?

to give gifts at Christmas

Arrakis is getting the Doctor a star shaped music box that plays the gallifreyan lullaby he learned from the Doctor, that way he can be comforted by the song whenever he needs it.

He was going to add a magic crystal from home as well, allowing the Doctor to use a bit of his magic to create simple magic and visual illusions with his imagination but he can't charge the crystal now that he doesn't have his magic. There is an empty slot for the crystal built into the music box though so it can be added later when he gets his magic back.