Credentials are irrelevant, Mr. Nobody can publish in Nature if he has the results that merit publication. But anyway, I'm an expert in statistical physics and qauntum field theory. I know a lot about probability theory, but I admit that I don't have a lot of hands on experience with handling huge amounts of data. I've just completed my Ph.D. and I've published 15 articles in peer reviewed journals.
"So you are completly wrong."
No, because credentials are irrelevant, only the results and argumentations count. Prof. Dr. X can be wrong and Mr. Nobody can be right. This is how science works.
"the probability of obtaining a result at least as "impressive" as that obtained, assuming the truth of the null hypothesis that the finding was the result of chance alone."
That's what I said all along (you assume the null model). In this case, all you've said is that probabilities are not as low as required to rule out a model. But that model is not the favored model that climate scientists assume. Your results would be much more interesting if you turn it around and show that Australia's temperature trend is significantly below that of the global trend. Because then you rule out the standard climate scenario with 95% (or higher) probability, assuming what the climate scientists say is happening for the rest of the world.
That would be a very important result that you can perhaps publish in Nature. Otherwise you have a (literally) insignificant result. You usually cannot conlude very much from the fact that some probability is, say, 0.3 and not as low as 0.05. assuming some model. It is neither strong confirmation of that model (because you started out assuming that model to be true), nor is it evidence that that model is wrong.
It shouldn't be so difficult to subtract from the data you've used the global trend and see if there is a significant downward trend. That could well yield a significant result, in which case I look forward to reading your publication.
