I made the same assumption and didn't even try putting the dog and rabbits together, but I completed the puzzle (at least I'm pretty sure I didn't overlap them, there was a lot of back and forth)
I find it amusing that this is driven by the particular visualisations of the characters. I.e. if it were a chicken and a rabbit would you have also made this assumption?
For me it's a variant of a classical "move a wolf, goat and cabbage across the river", where you can't have some of them on the boat together, because it would be eaten.
