Do I save the
Users/username/Library/Application
Support/iWeb/Domain file and put it on my computer at
home that has the current published site and this
should replace that one?
Yes, as long as the Domain file has both sites on it. If neither of your Domain files has both sites on them, you will need to either switch back and forth between them or redo one site so you have both in one file.
Do I
have to have (bring home) all the pictures etc, that
I used for the website I created at work or are those
files all on my idisk?
All the stuff you used for a site is in your Domain file. It's presumably also on your iDisk, but that can't be used directly by iWeb.
I'm sure I don't, but I
better ask befor I leave here and have to drive all
the way back.
You might want them if you wind up needing to recreate your site from scratch. But you could always get them from your iDisk anyway.
Good luck with the project!