What is the safest way to move the iTunes Library from one hard drive to another?
You're actually on to the right approach. This Apple support article details the following approach for Windows (and this is the approach for a Mac user):


Open iTunes.
Choose Edit > Preferences.
Click the Advanced tab in the Preferences window.
Select the "Keep iTunes Media folder organized" checkbox.
Click OK.


If you haven't been letting iTunes keep your media organized up until now, you'll have to wait while it sorts everything out. Could take a few hours. Have beverages handy.

Once it's done sorting things out you can change the location of the iTunes library and iTunes will shuffle everything over to the new spot. From that article:


Open iTunes.
From the Edit menu, choose Preferences.
Click the Advanced tab in the Preferences window.
Click the Change button in the iTunes Media folder location pane.
In the Change Media Folder Location window that appears, navigate to the location where you would like your new Media folder to be created.
Click the Make New Folder button in the Change Media Folder Location window.
Enter the name of the new iTunes Media folder.
Click OK in the Change Media Folder Location window. Click OK in the Advanced window.

For iTunes 9 and 10: Choose File > Library > Organize Library
For iTunes 8: Choose File > Library > Consolidate Library
For iTunes 7 or earlier: Choose Advanced > Consolidate Library.

A message will pop up.

For iTunes 9 and 10: Place a check next to "Consolidate files" and click OK.
For iTunes 8 and earlier: Click Consolidate.

After the folder has been copied, locate your original iTunes Media folder, and drag it to the Recycle Bin. Important: Don't remove the iTunes Library files that may be in the same location as the iTunes Media folder. For more information about the iTunes Library files, see What are the iTunes Library files?
Quit and reopen iTunes.

If you receive the alert: "The folder containing "iTunes Library.itl" cannot be found and is required. Please create or choose an iTunes library," you most likely moved the iTunes Library files. If this is the case, move them out of the Recycle Bin and back to where they were.
If you do not encounter the above alert when opening and closing iTunes, empty the Recycle Bin.



Circa iTunes 9.x I used this (nearly) same approach to move my library from my main hard drive on my iMac to my Drobo and can confirm that it works.