I think it would be better to say the Q are able to travel between realities, rather than there's only one Q continuum that exists across all realities.
Because the latter gets into some sticky philosophical issues.
If there's only one Q (e.g., the John DeLancie version) that exists across all realities, then that would imply they really are some sort of "higher power" in the Star Trek universe that came into existence through some way where they're detached from the natural order of our universe, instead of being native to this universe and just another species that somehow evolved into their abilities. Early TNG implies this, when Q seems concerned humanity will one day evolve into something similar to the Q.
Other species this question arguably applies to would be the Prophets and the Guardian of Forever, since the Prophets exist beyond linear time and the Guardian of Forever has the ability to connect to alternate universes.
Because the latter gets into some sticky philosophical issues.
If there's only one Q (e.g., the John DeLancie version) that exists across all realities, then that would imply they really are some sort of "higher power" in the Star Trek universe that came into existence through some way where they're detached from the natural order of our universe, instead of being native to this universe and just another species that somehow evolved into their abilities. Early TNG implies this, when Q seems concerned humanity will one day evolve into something similar to the Q.
Other species this question arguably applies to would be the Prophets and the Guardian of Forever, since the Prophets exist beyond linear time and the Guardian of Forever has the ability to connect to alternate universes.