Yes to the separate carrier, litter box and food. Good luck on keeping them out of each other's food, though. Although my two are grown, they are on different diets, but they keep eating out of each other's bowls, even though the bowls are in different rooms. I just don't let them get too much of the "wrong" food.

Just know that it may not be love at first sight; it can take time for cats to acclimate to each other. Keep them separated at first and let them get each other's scent. Cats are all about smell.