I personally believe that only animals with a rather big difference in male and female behavior can have trans thoughts. Dogs for example can be good boys or good girls, but in the end, male and female dogs play the same, run the same, bark the same, and act the same. Humans however built gender stereotypes so convoluted that people may think they’re in the wrong team, unlike animals who don’t consider males and females different teams in the first place.
One species where I imagine that especially the males could have trans thoughts are black widow spiders. This is because the female is way larger than the male, and females tend to eat the males during sexual intercourse. So if I would be a male black widow spider, I would most definitely be trans. Unfortunately, black widow spiders are not able to afford trans surgery in this economy.