First off, welcome to the boards Hyfrydle, and thanks for your support! Glad you like the game.
At this time, it is not possible for a demo version of the game to play multiplayer with a retail version of the game. I don't know of any other RTS games that support this, so this was not something that it ever occurred to me to add -- but, given your query, it instantly makes sense to me why this would be desirable, given the cooperative nature of this game.
I've added this for my to-do list for the next prerelease (for tomorrow), and will post here when that is in. When a demo player plays with a retail player, the time restrictions of the demo player will of course have to apply, but that will still let you easily try out the co-op for an hour without having to buy two copies on spec or something.
In the meantime, here's a workaround: You can revert your copy to temporarily running in demo mode by opening the game, going to Settings, and then copying the Game Data Directory (the textbox near the bottom). Go to that directory in explorer, and you will see a settings.dat file. Simply rename that to settings2.dat or something similar, and your game will revert to how it was when you first installed it. You'll have to redo your settings and set up a new profile, etc, but you'll be in demo mode and can play with your friend in that fashion. If you later want to go back to the full version, simply restore your settings2.dat file to replace the temporary demo settings.dat file, and you're back where you were.
This will only be needed until sometime tomorrow, but I just wanted to give you a workaround for the short term, just in case. Thanks again for your support!