I'll be getting my copy of Skyrim tomorrow, and in the meantime I bought the Dawnguard DLC from Game. Well, it emails you a code which you then redeem in the Xbox Marketplace to get the DLC. What I was wondering, is can I download Dawnguard and then get Skyrim tomorrow, or should I wait until I get Skyrim and then download Dawnguard? I just wondered because my downloading time is so slow and I want to know if I can get it out of the way or not.

Get Skyrim first and then download Dawnguard.

You need to install Skyrim first, then install Dawnguard after you know skyrim is up and running.