What make and model is the laptop?
I have a "clean" partition image of XP that I use when my PC crashes - it has a full install, but no drivers loaded - when I do a full restore then boot on the HDD, XP will then install all the drivers for whatever PC hardware setup the PC has.
A few ways I can think of are:
Get an image of an installed/backup XP image (like Acronic True Image) onto the laptop HDD - this can usually be done by hooking up the laptop HDD to your desktop PC, and restoring - then hook up the the laptop again and boot - you can then load the drivers via USB stick.
Otherwise hook up the laptop HDD to the PC, disconnect you current boot HDD and then load XP onto the laptop HDD - when it comes to the driver installation, just cancel each one until the setup is finished - connect back to the laptop and boot - laod drivers from USB stick.
Make a smaller bootable partition on the laptop HDD, and load the full XP image/files onto the bootable partition - insert HDD back into the laptop, then select that partition to boot from and install to the larger partition.