Hi, Gee -
As Tom indicated, OS 9.1 is insufficient for your G4 dual 1GHz model; it can't boot to that early an OS.
If your machine is a QuickSilver, it may have come with a separate OS 9.2.2 Install CD. You should be able to boot the machcine to that CD and install OS 9.2.2 directly onto the 20GB partition.
***
However, if your machine is an MDD (Mirrored Drive Door) model, the machine came with a combination install disk set, one that boots to OSX but which can also install OS 9.2.2 (Classic). Unfortunately the installer will insist that Classic (OS 9.2.2) must be installed onto the same volume (partition) which contains OSX. This is inconvenient, but not unsurmountable.
Go ahead and install OS 9.2.2 onto the OSX partition. Once that has been done, boot the machine to OS 9.2.2 and then drag the OS 9 System Folder to the 20GB partition and let Finder copy it there. Do the same with the OS 9 supporting folders (Applications (Mac OS 9), Documents, and any other folders specific to OS 9).
Make sure that the Mac OS logo/glyph appears superimposed on the System Folder copied to the 20GB partition - this indicates it is blessed, meaning it has been recognized and flagged as a bootable OS.
Then test boot to the copied OS on the 20GB drive. You can do that using Startup Disk control panel, or using
Startup Manager.
OS 9 is easily copied this way, via a simple Finder drag-and-drop copy process; cloning is not needed. Usually such a copied OS 9 System Folder is usable immediately.
Once the test boot confirms that it works, you can remove the originally installed OS 9 on the OSX partition. Or, you can retain it for use as Classic, keeping the one on the 20GB partition for dedicated use as a bootable OS.
***
In either case, either machine model, in order to be able to boot OS 9 from a volume the volume must have had the OS 9 drivers installed.
The OS and installer on a stand-alone OS 9 Install CD will not be able to 'see' any volume which does not have OS 9 drivers.
The combination disk sets, such as come with an MDD model, will be able to install OS 9 (Classic) onto a volume which does not have OS 9 drivers, since the installer is run by OSX. Such an install will be usable as Classic, but not as a bootable OS 9.