I am about to receive my diploma in screen and media from a specialized 3d game art course, and am lined up for another year of study for an advanced diploma. Should I start looking after I get the advanced diploma, or keep studying for a degree and then start?

Australia. I don't think most of our full-time courses even last 4 years.

There are two concerns.

First, you don't exist in a vacuum. You compete with other people for the job. If other applicants have degrees and you don't, you can guess who is first to be interviewed. Same with having demos and completed prior projects or having industry experience. Not having them doesn't mean you will never be called, but it may mean you're not in the first round.

Second, education is not job training. Education forces people to study topics they wouldn't normally study on their own, and a degree asserts that graduates have achieved a basic mastery of a certain breadth of topics. But that's just a starting point. You will be expected to learn and develop and grow on your own far beyond what it took to graduate. Think of it much like how doctors and lawyers must constantly keep their skills updated; a doctor who doesn't study about medical techniques and new drugs for decades will be outdated; a lawyer who doesn't keep up on new laws and court orders will quickly find they're outdated. The same is true in games, all disciplines must constantly improve and study.