This is the point at which you should really be using your console. Right-click (ctrl-click on mac) on the page, and pick "inspect element" or press "ctrl-shift-j" (cmd-shift-j on mac) to bring up the dev console. Make sure you're on the 'console' tab, and then look for any error messages. Specifically, you're looking for any '404' errors, which tell you that the browser tried to find a resource in a particular spot, but couldn't.
You should see at least one error: the getElementByIdea method is on the 'document' object, so you need to do:
document.getElementById('image')...
and not just
getElementById('image')....
Fred has a good idea here, but I don't think it's the issue: if you load the script before the rest of the page, the script won't be able to access the DOM elements loaded after it (sort of). However, each time you run your doStuff() function, you're essentially telling the script "hey, look for that element with id 'image' again!", so this shouldn't matter here.
It is, however, generally a good idea to load all scripts that modify the DOM in some way at the END of your page, as Fred describes.