game.pov.currentcommandresolvedelements
(objectdictionary, I think) will contain a reference to all objects (including exits) in the last command. So in the case of a "go" command, the key "exit" would give you the exit passed through.
However, I suspect it would be less prone to bugs if you gave the rooms above and below a script (on exit? Or when you enter them?) which sets the location of the bunny people appropriately.
If you frequently want to know which room the player has come from, modify the player object's changedparent
script to save oldvalue
in an attribute somewhere before triggering the various scripts.