Oceania is an incredibly safe region to travel through. Violent crime and petty theft occur at low rates - although like anywhere, the risk increases in urban areas. If you follow the usual travel safety precautions and common sense you won't have any issues. The remoteness poses the largest risk to traveller safety in Oceania. If you do get hurt in the outback of Australia or on one of Fiji's outer islands, then it can be a long flight to get anywhere for help.