Anyones copy of Dominions 3 is capable of running in "host mode". You can run one copy in host mode, one copy playing the game, then have your friend connect to your machine and join in the play.
Or you can join with just the two of you into an open game that has AIs. You could start such a game for just the two of you on Llamas server if you wish to play using email to send in your turns.
If you would rather have a quicker, more like solo play, game then you could join one on the Dom3Minions server. There are 3 game types there with AIs. The vsAI, Srand, and Chaos.
http://www.dom3minions.com/HostedGames.htm
I would recommend starting with the vsAI games. You can both join, then hit the "start game" button to kick it off without waiting for other people to join.
http://game.dom3minions.com/bin/vsAI_chk.cgi
Read the "How to Join" link. It has tips such as.. you must use the game tools to create your god before joining. Its not like solo play where you start the game and then create your god. But once you figure out how to join a networked game like this it plays pretty much like a solo game.