I'm planning to relocate to Taiwan for business in two months. I would
like to ship my car, and I have a dog. My wife is from Taiwan. But we
can't seem to get solid info on the following questions:

1. Will the dog have to be quarantined (emotionally, we can't handle
that) so if yes, how can this be avoided.
2. Do we have to pay any kind of import tax on moving our car to
Taiwan? We need the vehicle there, but to me it just seems like
another item of luggage.
3. What's the best way to move the car (inexpensive)

I've seen a lot of websites, but not real-life experiences, no Taiwan
government, clear, regulations for our actual situation.

Where are you now?

How about buying the same model and year used car in Taiwan and then
selling it when you're ready to leave? I suspect that would be
cheaper.