Ummmm, I could be wrong but I thought
a) daughter's music is played on Creative Zen (and from what I read before posting a comment, it may convert to a different format before the file is saved to the music player device) and
b) OP's music (not DD's) is known to iTunes. Two separate sets of music, and lack of space on laptop being reason to explore storing music on memory stick(s).
I assumed that the wish was to move the DD's music off the laptop onto memory stick, but those tracks would be played on DD's mini-notebook as well as from the Zen player.
However, if the tracks have been altered from MP3 format, and/or the MP3 originals misplaced (after all, one might think that once in the Zen player, no need to keep them, if space was getting low on the OP's laptop) then there could be a problem trying to play what was available, on anything other than the Zen unit, unless there's suitable player software for the mini-notebook...
That was how I was reading it, anyway.