I don't know if it will work. Firstly the version for both has to be the same IE one cannot be XP Pro and the other XP Home they have to be the same, both Pro or both Home. And I am unsure never having done this whether it will pass validation as it should identify that all the hardware has changed.
The XP on the old laptop will probably be OEM and therefore won't transfer.
You could try it but I'm afraid I haven't a clue as to where to start.