Given Q's personality, the Changelings would seem a prime example of a species he would want to interact with, test and mess with. They have a god complex, like to manipulate and control other species and bring war on the galaxy. Has Q ever been shown interacting with any member of the Changeling species in any of the Star Trek materials?
I can't find anything about Q interacting with the Founders, or any Changeling besides Odo. Odo, however...
However, while Odo and Q both appear in this episode, they don't really interact. Q is interacting more with Sisko and O'Brien, while Odo is focusing more on Quark. As Odo is the security officer on DS9, though, he'll almost certainly know that Q was on board and will have been briefed on what he is.
As this is the only time we see Q appear in Deep Space 9, there aren't really many other opportunities for such a meeting to happen in canon sources.
If you include non-canon sources such as licensed novels, then The Q Gambit by Mike Johnson might be another place where Q and Odo meet; it's a 6-part comic story where the USS Enterprise is transported into the future by Q to meet the crew of Deep Space 9 (including Odo).