Can you think of a way to re formulate the puzzle so that you can express the rules without words?
Also, the dog / rabbit dynamic (as used in the classic dog/duck/grain river crossing puzzle) made me think that I had to chase the rabbits with dog, or that dogs and rabbits couldn’t share a node. Different animals might be better — rabbit and mouse, perhaps? Or even different coloured rabbits and different coloured carrots?
The words thing though — that’s what you should work on next, I think. Good puzzles like this are word-free in the puzzle itself (Stephen’s sausage roll, English country tune).
It would take this puzzle from great to excellent. Good luck. More please!