Hey, congratulations! These are great machines! The iBook G3 is among the first totally fresh NewWorld designs after that switchover. (The Blue-And-White G3 being a faster beige platform with the new ROM on it.) It gets some neat stuff like USB booting (volumes under 200GB) of Classic Mac OS and, well, they're nice machines in general.
I think with a drive of this capacity, things get a little weird because older computers don't really handle drives over 128GB very well at all.
I'm using a 2TB pocket hard disk on a PowerMac G4's onboard USB 1.1 port and it behaves what you'd expect of as "correctly", so this will definitely work. Mac OS 9 has a maximum
volume size of 2TB, I have yet to test larger maximum
disk sizes, however, on controllers that might support it (USB in particular because the real controller is going to be whatever the USB/SATA Bridge is). 120/128-ish gig limits as often cited for this era are going to be related to IDE on certain older systems. I've seen various reports of ways to skirt this but for an internal boot volume, 120GB is probably enough for a system like this. There's a separate "around 200 gigs" limit for boot volumes for Classic Mac OS, which does also apply to USB/Firewire devices.
I second the idea of reformatting or repartitioning the USB device on the iBook, if you intend to use it for backup or as swing space or for transfers. (unless you did that on the iMac, which you also mentioned and I missed on my first read-through, which definitely makes this a bit more of a stumper.)
The other thing, of course, is to make sure you're correctly dismounting the drive before disconnecting it, and stuff like that. You probably are, esp. since it works fine on your iMac.