If COVID can hang out in animals or on plants, we are kidding ourselves by pulling the FIRE alarm over every case.
My wife's a veterinarian, and keeps up with such things - at this time, as compared to passing human-to-human, animals are a negligible source of covid-19 infections. If you work with animals that are kept in close proximity with people (like, you're a veterinarian), then there's precautions to be taken. But you should worry more about whether Fido's owner is wearing a mask than about Fido.
Covid-19 hanging around on plants in your environment is similarly not an issue to worry about. Food items that have been handled by humans still ought to be washed, but you aren't going to catch it from the oak tree in your yard, or someone's lawn.