Better to do PhD program for Marine Science in Australia or US?
Quality of life is very subjective.  If you like nature, you will struggle to find the same quality of life in the U.S. as you do in Australia.  If you like big bustling cities, then your quality of life will be better in the U.S. than in Queensland (Brisbane is lovely, but hardly bustling).

People care more about the strength of the school in the Ph.D. subject than they do about the university overall.  If you intend to stay in marine science, it doesn't really matter whether you get a Ph.D. from e.g. James Cook in Australia or many places in the U.S..  If you're not sure marine science is where your heart is, a university with a bigger name overall will help you.  Australian universities are competitive internationally; it really depends what your choices are.  (U.Q. is not, say, Stanford, but I don't think there's anything in Florida that would really give you a big edge over U.Q.)