You need to do a system transfer. Nintendo has a nicely detailed guide on how to do this, but here are the important bits:
You need to have both Wii U consoles in front of you, and they both need to be fully updated with a gamepad paired to them. The source WiiU must have a Nintendo Network ID tied to it. Make sure both Wii U consoles are connected to the same internet network. When you are ready, start with the source WiiU (the one you are taking the data from), and go into the System Settings, scrolling until you see the "System Transfer" option.
From there, you can just follow the prompts - make sure that you tell it correctly which is the source (the one you are taking the information from) and which is the target (the new one the information needs to go to).
If done correctly, this will ensure all of the save data and so on on the old console goes to the new console. (It may have to take some time to download any content you have downloaded on the old console, but it should automatically set up those downloads.)
It will also ensure that the preinstalled game remains on the system so you don't lose it.
For the most part, the transfer is really easy, and there are lots of on-screen prompts so you know what to do along the way.