There are many boxes and baskets available for transporting cats. It is best not to get the solid sided version as these are not too pleasant for the animals to enter. A wire basket with top opening for ease of access may not look so attractive but has better vision all around and is easy to use.
"The great charm of cats is their rampant egotism, their devil-may-care attitude toward responsibility, their disinclination to earn an honest dollar."
~ Robertson Davies