How to introduce a sweet cat to a dominant beagle?

[Dalia(I)]

My dog KL is a dominant beagle and is the princess of the household. My family is thinking of getting a tabby cat and we would like to bring the dog to the humane society to meet the cat, but KL is afraid of the car and we're afraid that she'll have a spaz attack, hide from the cat, and not act like her usual dominant self.
What should we do? How should we introduce the cat to the beagle. Also, KL doesn't like cats very much because the WAS a hunting dog, my dad encourages her to chase moles, squirrels, cats, and birds.