If you are going to have them outside unsupervised for a while, you need to have a run that has mesh on both the bottom and the top, that way they can't dig or jump out and nothing can jump in to eat them. You will also want a solid, secured part that they can hide in or snuggle in if they get scared. Also consider that it will either need to be in the shade, or you will need something to cover it to protect from the sun and the rain, rabbits overheat very easily outdoors in summer.
As for the wild rabbits and diseases, there are two that you need to worry about, myxomatosis and calicivirus. Unfortunately, only calicivirus can be vaccinated for in Australia and must be done annually. Both are mosquito born diseases so even if you vaccinate for one, I would still strongly advise securing flyscreen to the outside of any hutch or run you get for outdoors, especially since you say you have wild rabbits present, where therefore the risk is greater.