First, you can't really install windows on a removable drive straight out of the box like that. There are discussion threads here about this. Second, if you install XP on one system, then transport it to another system it will almost 100% of the time not work, unless the hardware is exactly the same. Once again, this has been discussed here before, but is a good amount of effort required to make it work.
Your best bet is to do it the proper way, and get a CDrom drive. Perhaps remove it from your desktop and plug it into your carpc temporarily for the install?