Amanda Rogers' parents (who were Q) and the Douwd known as Kevin, were on earth pretending to be humans at the same time. Given their powers, it does seem likely they were aware of each other.
So are Q and Douwd aware of each other?
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The short answer is that we don't know. There is only one mention of the Douwd in the TNG series (in Survivors) and no further mentions of them in any canon property including the other TV series, films or canon 'ongoing' comics.
Moving down the food chain into the EU novels and comics, the answer is we don't know. There are only the most glancing references to the Douwd in any of the Extended Universe novels, and always only in the sense of "powerful beings like x" (where x is the name of a being such as the Organians, the Q or the Douwd)".
We don't know. Certainly the Douwd are very powerful which potentially makes them interesting to the Q. The flipside is that they may have sufficient power to somehow hide themselves from the Q. I lean toward the fact that the Q known as Quinn makes it abundantly clear (in Voy: Deathwish) that the Q have been everywhere and seen everything. That presumably would include knowing everything about the Douwd that there is to know.
Logically, both the Q and and the Douwd must be aware of one another as they both exhibit omniscience. If a Douwd could destroy every Husnock individual in creation, he would need the trait of omniscience.
Q is able to manifest at will across spacetime in any direction (All Good Things...) which also implies an ability to 'omnisce.' There is literally nothing he cannot observe anywhere or anywhen at any time.
On the other hand, just because these entities CAN know everything, doesn't mean they DO know everything. They can also choose NOT to seek out knowledge, in theory.
And is it also possible that a 'greater omnipotent-omniscient' could cloak itself from a 'lesser omnipotent?' Maybe... But regardless of whether the Q Rogers were aware of their proximity to Kevin Uxbridge, the Q Continuum likely know of the Douwd and vice versa.
But the original question begs a larger question:
In 'Encounter at Farpoint' and 'True Q', Q makes it clear that the Continuum consider themselves to be moral superiors. One aspect of this is their restraint from abuse of their powers. They, like the Organians hold themselves to be the judges of 'lesser' races.
So if the Q or Organians would judge Terrans for their historical wars, it seems odd that they haven't dropped the hammer on Kevin Uxbridge, if they are indeed superior to the Douwd. So either:
The Q are less powerful than the Douwd: and can do nothing to them. (Kevin maintains that he is immortal and cannot be destroyed).
The Q are coequal to the Douwd, and can do nothing to them.
The Q are more powerful than the Douwd, and CHOOSE not to hold them to account. If this is so, then it implies all their threats against humanity could well be hollow and calculated solely for effect. All we really know is that they are willing to exact capital punishment on their own, as they kill Amanda Rogers' Q parents for abusing their powers.
So the ultimate question may be: Can the'Galactic Gods of the Milky Way police each other?'
If Kevin Uxbridge decides one day he want to blow up the Milky Way, would the Q have anything to say about it and vice versa? The Q enforce law against their own, but the Douwd clearly have done nothing against Kevin.
While the Organians, Q, and Douwd demonstrate very 'strong wills' to resist the death impulse that might lead them to blow up the universe they are AWOL when their coequals go off the rails.
Proof: the Q civil war blows up a number of star systems. Neither the Douwd nor the Organians intervene.
The Douwd genocide of the Husnock. Neither the Q nor the Organians intervene.
So this suggests that the same tenuous balance of power that exists between nuclear powers also scales up to a stalemate amongst these 'omnipotents' as well.
I think these 'Omni's' must be quite aware of each other but seem powerless to intervene against one another or are afraid to play the galactic finger wagging game with one another as they do with lesser species. Perhaps such a conflict would be even more disastrous.
But given that existence is just a state of quantum possibilities that these omnipotents can traverse at will, maybe creating one universe where the Husnock disappear, while continuing to exist in an infinite number of other universes means that these beings really don't take existence too seriously.
Kevin Uxbridge's guilt, therefore, like his pacifism, is a pure affectation. He could just as easily have recreated the Husnock as destroyed them and maybe he will in the future when he has paid his penance and none will be the wiser. Maybe the Q know this and have moved on. And his interaction with the Enterprise is just a kabuki object lesson for their benefit and his own self-flagellation.