If you download the ISO, then as far as I am aware you can install it on another computer at any time you like, presumably this also applies to burning. I can't envisage any time limitation on burning the ISO.
If the Vista laptop is 32 bit and the Xp desktop is 64 bit then no. You will end up with the 32 bit version only. If both 64 bit then yes. You can also download the iso to the XP desktop, copy to usb drive then use the laptop to burn the ISO to DVD.