Hi
128MB of RAM is not enough – you should have the full 1GB that that eMac supported for any real work.
It will run FCP v4.1.1 or v4.5 HD if you update it to Panther OS X 10.3.9 – it might work with Jaguar 10.2.8 but nothing before 10.2.6 was any good at all.
QuickTime can be v7.1.5 even if you find that FCP v5.0.4 or much better v5.1.4 will not overpower it.
All these were/are stable versions, but a lot of the other interim versions were not fully reliable.