Our rabbit lives in our garden and we have seen some rats out there. Can they pass anything onto the rabbit? They are not big dirty sewer rats, just small fluffy ones, but do they still carry disease?
Approximately 50 - 60% of those 'small fluffy ones' as you put it can carry Leptospirosis or Weills disease. Apart from infecting your rabbits they can also pee on their food or bedding and pass on salmonella. They can also pass all of this to you if you handle anything they have been on. They are also likely to eat any babies or young rabbits. So basically, get rid!