You can ask two specific questions about the presence of an animal. "Is the dog a service animal required because of a disability?" and "What work or task has the dog been trained to perform?"

I would think Uber would want to handle those sort of compliance issues before the driver gets there. As you don't want the driver to get something wrong. And it just makes things smoother for everyone.

Not sure if they can require a rider provide this information ahead of time, before pairing a rider with a driver. But if its voluntary, I don't see any problem with making the process smoother for everyone. Again IANAL, so could be off base though.