I do not think that the Q are Gods. Whatever Voyager made of them, in TNG it's implied that a lot of the things Q does just amount to illusions (and there's nothing shown on Voyager that would really contradict this) and you can live on illusions.
The Q are powerful, yes, within the laws of the universe, but I can't really see them survive the death of those very laws of the universe.
Not quite.
Per VOY, we know the Q have control of space, matter and time (which of course doesn't make them gods in any kind of capcity of course).
They can also travel to other universes... so it would be conceivable that if the existing universe ends, they could just go to another one.
Mind you, we don't know if the Q continuum is explicitly linked to the universe of Trek prime timeline in a way that the death of the universe would mean the end of the Q Continuum as well.
From what I gathered on VOY, we know that events in the Q Continuum can affect the universe (in the form of supernovae explosions for one thing)... and while we know that you can access the Continuum from the universe (by using a supernovae because a negative density vacuum is created during the sun's explosion which then sucks the surrounding matter into the Continuum - which is how the female Q got VOY into it), but we don't know if death of the universe would have an effect on the Continuum... from what we could tell, I don't think so.
It seems more like the Continuum is an upper branch that monitors the multiverse of sorts (and the multiverse would be connected to the Continuum as such and rely on it somewhat, but not the other way around)... so if one universe dies, I don't think it poses a danger to the Q Continuum - especially when alternate timelines and universes were created and ceased to exist due to time travel... without the Continuum being affected.
A bigger question would be can the UFP escape the death of the universe?
Answer is... yes.
They already demonstrated they have the tech to breach space-time and cross into other universes... but putting that aside, if UFP became a fairly advanced Type III civilization on Kardashev scale (aka, on its way of becoming Type IV), it could conceivably generate more than enough power to shift whole galaxies from their universe into another one that's young (though I suspect the whole UFP would end up evolving into energy beings way before the universe ending becomes even remotely an issue - and at that point, they will probably have same or very similar capabilities as Q - but prior to that, they'd be technologically assisted proto-Q of sorts).
