Run iTunes without it being in the dock
Solution 1:
The only way for an application to not appear in the dock (while also keeping the menu bar) is for the developers to place that functionality into it. I don't use my dock as a launcher, using Butler instead (which is a dockless application, btw).
You might try backing up a step and asking why you want to remove the iTunes from the dock and see if there's another solution. For example, I often listen to tunes on my iPhone rather than iTunes. If it's to keep the dock clean, try a different launcher than the dock and hide the dock instead.
Solution 2:
From HERE. I have not personally tried it with iTunes, but it does work with some applications.
If you'd like to have an application running, but without a dock icon, there's a
way achieve this by modifying the application's plist file.
Open a terminal session, and first navigate to the "Contents" folder of the
application you'd like to modify (note - you may want to make a backup of the app
first, especially if it's one of the Apple-installed applications). This example
uses Key Caps:
cd 'Applications/Utilities/iTunes.app/Contents/'
Now, edit the Info.plist file:
vi Info.plist
You can use vi, pico, or emacs to do the editing.
Just before the closing Just before the closing </dict> tag, add
<key>NSBGOnly</key>
<string>1</string>
Save the edited Info.plist, then launch iTunes from the GUI
(your application foler). If your edit was successful, you should see iTunes,
but no icon in the dock.