The simplest answer to this question is; It's not made clear

In general terms, the Q appear to be able to move freely in time and space, potentially to any point within the universe, and certainly to travel within their own lifetimes. Q seems to have an awareness of the future actions of his fellow Q (Quinn) and has absolutely no compunction about sharing that knowledge with him in the episode [Death Wish][1];

> **Q :** *In the Continuum, an individual has an obligation to be responsible **to the path his life will follow.***

On the flipside, after the death of Quinn it appears that Q and the rest of the inhabitants of the Q continuum are cast adrift from the knowledge of their future actions. They fight a bloody and destructive civil war between the forces of order (who want Qs to ensure that they remain true to their future actions) and the forces of individualism who seem to want the Q to have the ability to create paradoxes by not doing so. In the grand scheme it's not clear what the outcome of the war is or how it will affect individual Qs


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**Update** : In the endnotes for the IDW comic "[The Q Gambit, Part II][2]", there's a brief description by series writer Mike Johnson about the nature of Q.

> Q. ***If "Q" is omnipotent, does he view time as linear? My point is. will
> he "remember" Picard and the TNG crew or is this his first contact
> with humanity?***
> 
> **MJ:** *...I think (from my poor little human perspective) that time is
> not linear for Q. We see it as linear with one moment leading to
> another creating a past present and future. **Q (again, in my
> interpretation) sees time (and three-dimensional space) more like you
> and I would see a map. It's all there in front of him, and he can move from place to place the way our eyes jump around a map.** Q likes to have fun moving 3D
> organisms around the map and seeing how they react (e.g. Picard in
> the TNG pilot, and Kirk in this story).*



  


  [1]: http://www.chakoteya.net/Voyager/210.htm
  [2]: http://en.memory-alpha.org/wiki/The_Q_Gambit,_Part_2