The 1.2 and 1.33 Ghz iBooks can be upgraded to 10.5.x Leopard maximum.
Mac ibook g4 free download - Apple iBook G4 Graphics Update, Apple iBook Firmware, Power Mac G4 ROM Update, and many more programs.
The Lack of upgrades to OS X 10.3.5 is probably due to the lack of Apple support for the older systems through software update. I found a link for you to try a direct download of the 10.3.9 updater.
I have an older iBook that can only run 10.3.9 and the internet experience is awful. It is slow and the screens are sometimes screwed up as you have experienced.
To adequately use the internet you should consider upgrading the RAM. 256MB is barely adequate and the upgrade price is pretty cheap. OS X 10.4 and 10.5 need more RAM than the 10.3.5 you currently have so a system upgrade only would not increase performannce.
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(The maximum memory capacity of this system is 1.25 GB with 256 MB onboard and a 1.0 GB SO-DIMM.)
Regarding OS X sources there are no downloads available for 10.4 or 10.5 so you would need to purchase a copy. It would need to be a retail disk(s) as there were no original install disk(s) for your iBook other than 10.3.
The links below are to some dealers but some of the prices are absurd. Ebay can be a source but be certain the disk(s) are the retail (BLACK) and not (GRAY) intended for another Mac.
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