Awesome. I love Eberron. You're making a good choice.
There is another 4e Eberron themed adventure: Seekers of the Ashen Crown - http://www.wizards.com/dnd/Product.aspx?x=dnd/products/dndacc/9780786950171
- I haven't played it myself though. There are also a few free adventures from Dungeon you could adapt: http://www.wizards.com/dnd/Archive.aspx?page=1&sort=category
As for DMing, the main advice I have is try not to sweat it too much. You can feel you've done a lousy job and still have your players tell you how awesome stuff is. Focus on a small part of the world (e.g. Sharn, Aundair, etc.) and read up on it. If you set your first few adventures in the same area, you'll have less to keep track of and your player will learn the setting quicker.
For more specific advice, I'd go to an office supply store and get a few sets of tabs. Tab the skill challenge section in the DMG and put tabs on the monsters you plan to use before the session. I also like to use a small dry erase board to write down monster HP and status, initiative and all that other stuff - once the fight is done, I just wipe it clean and its ready to go again.
With one player, you'll need to tone down fights. Usually this means one 'real' opponent and a couple minions. The Dragon Annual has a chart showing the best opponents based on the PC's role:
Controller: Artillery*, Controller, Skirmisher
Defender: Brute, Skirmisher*, Soldier
Leader: Controller, Skirmisher*, Striker
Striker: Brute, Skirmisher*, Soldier
* = Ideal role
You don't have to stick to this, but it is a good list of what 1-on-1 battles produce interesting fights. If the player loses a fight, usually it's more fun to have them captured and get to make a daring escape than to just kill them. It keeps the game from ending too. If you want to have a larger fight, you can balance things out by adding some guards or soldiers on the player's side to help them out. This is especially fun if they're playing a Warlord or Bard and need others to get the most of their abilities.