Just to reiterate: OS X versions newer than what came with that model will work just fine.
The dual 1 GHz MDD came with 10.2 installed, so if you have a retail 10.3, 10.4, or 10.5, it will install with no problems whatsoever. You would only run in to issues trying to use a retail 10.2, or 9.2.
This being 68kmla, I was kind of assuming you were talking about putting the oldest possible OS on. If you want it for real current use, it will work great with 10.5. (I have a G4 Digital Audio with a dual 1 GHz upgrade, and it rocks. Faster than my 1.25 GHz eMac for almost everything, in spite of the slower bus, slower RAM, and slower single-core speed. (They have nearly identical hard drives.)