One thing about rabbit fur is that it tends to wear out fast. You could try it, but you might be replacing it with something else before long.
I haven't made any mocs before (on the to-do list), but I would think that contact cement would work ok for attaching a sole (maybe rawhide?) that could be replaced. I could be wrong, but I don't think that moisture would affect the glue much, and it can be pulled apart when the time comes to replace it.
These are just suggestions, maybe someone else with more experience will chime in.