So basically, I just download either CCC or SD onto my laptop, then clone a copy of it onto my external hard drive. Right?
I just have one other problem I didn't mention. I don't know if I can restart my laptop by just holding down the option button to select the startup drive. The only way I could start it today was by resetting the PRAM. I'm afraid if I turn it off at this point I may not get it going again. Can I select the startup drive by using the System Preferences and clicking on "Target Disk Mode" ?
Once I have the external as the startup, it woh't matter if my laptop's hard drive fails, will it?
Depends on what we mean by 'start'. I cannot recall all the troubleshooting I did a few weeks ago before I gave up on my Pismo after installing a new RAM module from local Apple reseller (heh, maybe I shorted out the CPU daughter card, with static electricity, or the hundreds or so micro sized gold plated pin contacts were lose for the CPU daughter card socket?) and just ordered a TiBook to replace it. You can boot to a certain point in the startup procedure, even with a HD not installed (forget how far you get, but basically on my Pismo, I had the system booting up and then shortly thereafter it would freeze and shut down like the power supply wasn't working), I disconnected my Pismo HD (every easy to do on that model, not so on later models) and tried holding down the option key to get a flashing folder ? icon, but I could not get farther than the startup chime sound. Transfered the 133Mhz RAM module from the Pismo to the TiBook, so I know I did not kill the RAM with static electricity installing that, something else like logic board failure or PS failure was keeping it from starting up. Meh, I needed to upgrade anyway, Tibook is so much nicer than the old Pismo, much brighter screen, just fan runs almost all the time with a 1Ghz G4...this will last me until OS 10.6, then I have to give up booting into OS9.2.2 (yeah, I have issues).
Almost sounds like the PRAM battery is going bad.

Could be, but OP says DU says HD is failing...which may, or may not be accurate

If it is in fact a HD failing, installing a new one is a nightmare proposition compared to other models...basically you have to do a full tear down of the system to get at the HD. Better to have an authorized Apple repair facility do this install. Unless you
never plan to use the iBook for it's portability, you are going to want to have a bad internal drive replaced.
Guild to DIY ibook HD replacement, read it and weep:
http://www.ifixit.com/Guide/Mac/iBook-G4-14-Inch/Hard-Drive-Replacement/84/15/
One thing that no-one has mentioned yet is that to make a bootable drive for a PPC Mac, it's got to be partitioned in Apple Partition Map.
Once partitioned that way, it will not be bootable for an Intel Mac until erased and partitioned in GUID Partition Table scheme.
These options are in Disk Utility>Partition>Options along with Master Boot Record...
But the OP has a PPC G4, can you select an GUID Partition scheme from DU when on a PPC, or does DU determine if your system is a PPC, and only allow APM?