Best bet is just do a complete folder dump from your regular Dominions computer onto your laptop. Safest way to make sure you don't leave anything behind I find. (although be careful if you are using Vista, as that likes to randomly hide things)
I installed the game on my laptop, copied over the maps and savedgames folders (don't use mods), and tested out the previous turns of my 4 MP games. Everything works fine! Thanks for the help!