Maybe this?
post 4666
I don't have local times for either post so may well be wrong.
If somebody was ill then Perth sounds sensible as it has well equipped hospitals. I don't have the runway details for Broome or any of the other airports along that coast to hand apart from Truscott which has an enormously long runway but is situated right out in the bush miles from any facilities. From memory all the rest would require an onward flight courtesy of the RFDS. Remember, it is some time since I have been out there so all of this may have changed.