Odo not having the disease is a continuity error. Since it's said later that he got the disease from Section 31 during season 4, you're right that he should have gotten sick. You could explain it away by saying that something on that planet cured Odo of the disease. Like the writers, I guess no one at DS9 remembered that particular detail and so they never thought to attempt to look for a cure on that planet.
Here's what I don't get about this argument... Children of time aired during season 5. The changeling disease was not mentioned until season 7 (maybe the end of 6 at the earliest but I don't think so). So perhaps the writers just hadn't made up the whole changeling disease when Children of Time was written, ergo there is no way ' Gaia Odo' could have had it. Yes, if this was all real Gaia Odo should have been sick or even dead from the disease. But saying he got it during S4 was just a retcon by the writers anyway which created a plot hole that didn't exist when COT was written.
I think sometimes we forget that this is just a TV show, after all