Poor TinyBaci! Lucy can sympathise, when she was a puppy she was sick in the car more often than not.
We got round it by taking her out a lot, but driving really slow and gently so she got used to the motion. We also made sure it was a while since she had eaten a lot so that her tummy wasn'y so full. I think a car seat is a great idea! Madam though has a car harness, so sleeps on her blanket while we are on the move!