Depends where you want to go. Their winter is probably the best time to visit the tropical areas - drier, not as hot.
Elsewhere spring and autumn are probably best.
I visited Australia the first time in their winter (August/September) and though it was fine for going to the Great Barrier Reef near Cairns, Alice Springs and Uluru (Ayers Rock) (no flies then) it wasn't so good for Sydney (absolutely poured down first day), Melbourne, Adelaide and Tasmania. Next time we went in their Spring in the south and it was great. As dzug says all depends where you want to go.
summer is best in NZ, Jan-April. SE Australia the same but a longer season, say Nov-June. Perth pretty much anytime, I think. Darwin is hot all round but driest from May to Sept, wettest from Dec to March
Depends how hot you like it. Its quite nice here in New Zealand at the moment - about 20 degrees on average. Nice but not too hot. Jan/Feb it gets really hot! Australia is generally hotter than here whatever time of year it is, but it can reach temps in excess of 40 deg.