I'm not so certain that an omnipotent being like Q would consider the human race a bunch of pets. No, once there's a certain level of sentience, there is a degree of appreciation and respect.
But how do you define sentience? Modern cognitive science is increasingly demonstrating that sentience is a continuum, that many animals show a greater degree of self-awareness and cognitive complexity than we have recognized or been willing to admit. There's abundant evidence to demonstrate that great apes, dolphins, and maybe elephants are intelligent, self-aware beings, and yet our society still keeps them in zoos or circuses, and some keep baby chimps as pets. So even within our species, there's no consensus on what actually constitutes a level of sapience worthy of personhood. To a Q, humanity's ability to write books and build starships may be no more impressive than a chimp's ability to learn sign language or fish for termites with a stick is to the many humans who are aware of such skills but still dismiss the notion that anything nonhuman could be truly sapient.