But are they really?
From the DS9 Thread

Melk


cuiusquemodi

That's one of those Archimedal questions that makes my head hurt (like Janeway and time travel), but I do think that they could rewrite physical laws. They can take any form - not just appear as human, or animal, but actually BE that form. They are essentially non-corporeal.

The Q always remind me of the Lylmik in Julian May's Galactic Milieu books, if anyone has read them. All-powerful mental immortal beings, but so ancient, unchanging and torpid that they're degenerating.

I like to imagine a direct line of Q development which goes like this:
Q/Quinn is an unusual member of the race who begins to question things and wants to commit suicide.
Q (Original flavour John de Lancie) is influenced by this but isn't sure what to do.
He is sent to do the stupid 'humanity on trial' thing (never really understood this, but maybe it's the Q idea of a joke) and is intrigued by Picard, sensing that he can learn something from him that he can take back to the rest of the Q.
He becomes a bit of a Q rebel, is temporarily stripped of powers, also warns the Federation, through Picard, of the Borg threat (in retrospect, I think the Borg were coming anyway and this way meant more time to prepare, rather than that his actions alerted the Borg to the Alpha Quadrant - after all, they'd already assimilated Seven of Nine and parents).
Later on he takes up with Janeway, perhaps influenced by his own isolation among the Q which is similar to her being so far away. Possibly the fact that she also ends up facing down the Borg is significant - the Borg, though different from the Q in that they're very active and invasive, are similarly neutered, non-developing, uncurious beings.
Having a 'child' with 'Female'Q (and sometimes I wonder whether 'Young'Q was actually a being or just a projection of an idea, in the way that the 'war' of the Q was) is an interesting choice - Q/Quinn thought death would change things - OriginalQ thought birth would - both biological concepts (again, reverse of the Borg).

Does this make any sense or am I trying too hard to stitch things together?

In Deja Q, Q suggests that he has that power. Data and Geordi need to alter the path of an asteroid and Q tells him to simply change the gravitational constant of the universe. When they ask him how, he says something like, "you just do it."

Of course, Q, in his eternal arrogance, might have just said that to impress them. I've not seen that one. Does Q change the gravitational constant of the universe? Were he to, pretty much everything in the universe would shake itself apart.

In a book I recently read, "To Explore New Life: The Biology of Star Trek," Athena Andreadis analyzes the shapeshifters to see if they could truely exist. This is relevant because as she states, if a Founder takes the shape of a chair, where would its brain be. Likewise, if a Q took the shape of a lower animal, be it a deer, cat, or Human, where would it store its omniscience? I'm not sure. The Q raise more questions than answers.

But there's one thing I've seen done by the Prophets I've not seen from the Q. In the DS9 episode Accession, Akorem Laan is returned to his own time and finishes his opus that wasn't finished before he went into the wormhole. However, Kira remembers the poem from its uncompleted form. Short of someone returning from a past to a changed timeline, people only remember the time line they are in. I would contend that the Prophets equal, at least, the Q in power but just are unable to directly intervene in things that happen outside the wormhole, due to their restriction of existing in non-linear time.