An omnipotent being that made several mistakes? Fire without heat, food and drink without taste? He makes a mistake of the current era. A true Q wouldn’t make such errors. Spock even calls Trelane out on his mistakes, stating that he’s not omnipotent, that he only knows only forms of human society, not the substance. Kirk concludes that a machine is helping him and Kirk guesses correctly that it’s the mirror, due to the fact that Trelane never strays far from it.
Kirk shoots the mirror during a duel with Trelane and his powers for a time diminish. Yes he still had powers, but it could also be speculated that he had other devices on the planet. Trelane even at one point says to Kirk, “Did you think the mirror was my only source of instrumentality of power”. Eluding to that he needed technology to use his powers and he did in fact have other devices. I think it’s more likely that being he needed to use a device(s) that he could be of the same species of the god aliens from Pollux IV. They also had powers that were enhanced with devices. (TOS episode Who Mourns for Adonais) Being an omnipotent being, precludes error and Trelane makes many errors.
Q- Squared,or any other novels wouldn't count.The Star Trek franchise has always had the standing guidelines that it’s not canon until on screen, i.e. in a Star Trek televised episode or movie.
Milton made a valid point in Paradise Lost, about how the nature of God as traditionally presented as an absolutely good being; actually diminishes God's ability. Due to God being seen as good, God can only do good, and thus is not actually omnipotent in a functional sense. In fact one could argue that the Christian God almost doesn't qualify as intelligent or omnipotent, as that entity would lack the capacity to deviate from a rigidly defined set of parameters.
The Q, on the other hand, are functionally omnipotent. Not only are they capable of everything allowed within reality, they're capable of changing the rules of reality itself. They can choose to die as well as live, and they can choose to do good or evil. They can also produce baby Q's, meaning they theoretically still have the capacity to evolve to be even more powerful over time. Of course that's slightly problematic from a logical standpoint, but that hardly matters. The Q have the perfect solution to paradoxes; they just change the rules the rest of the universe is using. Trelane has none of those awesome powers!