This (veryvery interesting and insightful!) question is complicated by the difficulty of pinning down what the word "meaning" -- well -- means. Famously, the logical empiricist (i.e. "positivist") program of early twentieth-century philosophers like Rudolf Carnap and A. J. Ayers was beset by problems having to do with their definition of "meaning."
At the risk of homogenizing a very diverse and internally divided movement, a frequent assertion made by the logical empiricists was that the only statements that are meaningful are those that can be translated into a true or false claim about the physical world. One problem with this point of view is that it's not quite clear how this definition of "meaningful" can itself be translated into a true or false claim about the physical world. And of course if it cannot, then it is meaningless by its own definition!
Concerning your point about qualia, I might distinguish between our ability to treat a statement as meaningful and our intuitive sense that a statement is meaningful. Consider Noam Chomsky's intentionally "meaningless" sentence "Colorless green ideas sleep furiously," which is famous enough to have its own wikipedia entry. Upon first glance, this sentence may indeed seem to be meaningless, but people have attempted to argue that it is potentially meaningful in a number of different ways. Some of these attempts seem to overreach; they don't satisfy our intuitive sense of what meaning ought to "look like." And yet they allow us to treat the sentence as meaningful regardless of our intuition. Arguably our intuitive sense that a sentence has meaning has the character of a quale, then, but we may still be able to treat a sentence as meaningful even if the quale of "meaningfulness" is absent when we regard it.