Is there any way to move the "Save Document" icon (the one that installs at the end) in Word 2007. In XP space is very limited on the visible part of the toolbar so for me at least using the icon requires two clicks.

It depends. QAT modifications in Add-Ins are added after ones that are simply installed on your system.
Then they are in alphabetical order by the name of the Add-In.

If you want it earlier you can right-click on the button in the Add-Ins tab and tell Word to add it to the QAT. This will give you two, but you don't see the second one anyway. Word will add it to the far end of the modifications you've made, but by selecting Customize the QAT you can reposition those QAT items.

Modifying the QAT and Ribbon in Microsoft Word