Lol! Rabbits are anything but predators. Same goes for deer.
A lot of preds usually only come out at night, but even a neighbors dog can be a threat. I think a run is a good idea in any case. It is a safe area (hopefully) that your girls can use when you are not at home or they are otherwise unsupervised. It is also good for keeping them out of your garden & the neighbors yards. But as Bigz said, they also greatly enjoy their freedom. If you can let them free range sometimes, that would be great. But if that is not possible, I would try to get as large a run as possible so they don't kill all the grass, which they will do (it is just a matter of time).
How many birds do you plan on having?