I take it that you would be working in Port Moresby ??
Security and safety is a major concern in PNG.In Moresby expats tend to live in gated guarded communities with razor wire all around. It is not just local on local either.
You don't go out by your self, have to be very aware of where you are, don't flash money around, be careful when going to an ATM. Lock your car doors when driving around.
As for flying back to Brisbane on weekends the expense is prohibitive and not doable unless you employer is paying for it.
If you do decide to come over make sure your employer has a good medical insurance cover for you. You have secure accommodation. You have transport to and from your work location.
Unless a company is advertising specifically for an expat driver you will have no luck.
I have never seen any company advertising for expat drivers. The visa process is long and expensive.
There are many excellent local drivers available who have been trained by expats. Some of these are even better than some expat drivers I have worked with in PNG.
Living in PNG is no so bad as it gets portrayed. The violence is mainly between locals. General safety rules apply. You can get a flight to Brisbane for the weekend but will have to take Friday afternoon off and Monday morning off. Would be better to go to Cairns as the flights are better scheduled.