Yes they do. However there are far less of them than humans because they all die very early on in life. Animals have to face challanges that thanks to technology humans don't have to face like getting food and avoiding predetors. If an animal has a mental illness that interferes with these everyday tasks then they die. They might not be able to hunt as well in which case they usually starve, if we have a disability meaning we can't hunt it doesn't matter because we can get a job in which we are capable of and earn money to trade for food. Most mental disabilities affects these natural processes because animals have evolved the perfect mind for what they have to do and if it is changed slightly then they can't survive. This is natural selection or survival of the fittest. Mentaly challanged animals are not the fittest, so they die. By the way their disabilities are probably not exactly the same as humans so instead of autism they would have some animal equivelent.