Windows XP is licensed per processor socket, not per processor.
XP Pro entitles you to use 2 processor sockets and XP home one. The only systems which tend to come with more than one socket are servers or high-end work station that use Intel Xeons or AMD Opterons etc.
Anyway, all that means is you can have as many processors as you like so long as it's on one processor package. Thus dual core (or even quad or octo!) would work absolutely fine. Both XP pro and home are able to benefit from dual core exactly the same, XP pro for example wouldn't be any better than Home. Hope that explains it!