While i fully understand why caravans cannot go through moon gates, and otherwise cannot travel more than one room at once, i suggest the following :

When using the hunt verb, when hunting, and subsequently following up with an actual hunt to change rooms to find a critter, i suggest that the caravan follow the trader regardless of how many rooms were moved through.

I suggest this for traders that engage in creature combat and like to take their caravan with them to store the loot rather than carry it with them. This feature would make the current feature of being able to take your caravan hunting with you easier, less annoying, and actually desirable.

preemptive responses :
1. Since the maximum number of rooms anyone can hunt is 5 or 6 i think, the maximum distance a caravan would be every able to travel this way is the same.
2. It is unlikely that this would be abused for faster caravan travel as both hunt uses already have round times that equal about 3 or 4 room's worth i think (about), and it would require complex multi-character systems that would effectively make it less efficient to try to abuse, rather than just trade normal. (can you even hunt on the trade route? maybe some)
3. caravan following could be disabled if following up with a hunt to a person, could require a critter/non pc