OS 9 dos not require cloning software in order to copy a drive - a drag-and-drop copy is sufficient.
Add the new drive as a second drive - the G4 should be pre-equipped to accept a second drive. Jumper the second drive as Slave, and make sure the original drive is jumpered as Master (some Western Digital drives are jumpered as Single when there is no second drive, and need to be changed to Master when a second drive is added),
Format the new drive using Drive Setup - use the Mac OS Extended format.
Once the new drive is ready, drag the icon of the original drive to the new drive's icon and drop it in - the entire contents of the original drive will be copied to the new drive, and placed into a folder on the new drive; this folder will be named the same as the original drive.
Once the copying is complete, open the new drive and drag the System Folder, Utilities folder, Documents folder, and Applications folder out of the enclosing folder so that they are at the root level of the new drive (the root level is what you see when you first open the drive),
Make sure the System Folder displays the Mac OS glyph - this indicates it is "blessed".
If that's OK, then test boot to the new drive - use the Startup Disk control panel to select it, then restart.
Noye - some aliases may need to be 'fixed' on the new drive. This can include an alias to Sherlock in the Apple Menu Items folder in System Folder, a few items in the Application Support folder in System Folder, and any you may have created for your own convenience.
There are a couple of suggestions that I'd add to Don's thorough response. First, when formatting the drive with Drive Setup, I'd recommend partitioning the 120 GB Seagate into (2) or more volumes. I do so, because routine disk maintenance is much faster when the size of the playing field is reduced. The second volume could be used for archival storage or whatever specified use suits your needs. Second, I'd drag-copy the individual folders from the old drive to the new drive, one at a time. I'd start with the System Folder, then the Applications, then Utilities, Apple Extras, CD Extras, Documents, etc. If the old drive is experiencing problems, interrupting the cloning procedure like this, might prevent problems caused by an extended read from it. Also (as Don mentioned), you will need to check every shortcut/alias on the new drive (do a "Get Info" for each), because they will likely be referencing and reading the original target on the old drive. If both drives are connected, you might not think there's a problem, because the shortcut "works." With the old drive removed, the "original file can't be found" error message will be triggered, every time you click on a shortcut that you haven't fixed/updated.
Copying the individual folders works fine, too.
There is one difference, however - it's very easy to overlook individual items which are lying about on the desktop.
When you drag and drop the drive's icon, absolutely everything is copied, including anything on the desktop and anything in the Trash which has not been emptied; these items wil be placed in new folders named, respectively, Desktop and Trash, located inside the drive's contents folder on the new drive.
If you choose to do an individual folder copy, be sure to also copy the items left on the desktop.