October is the pre-monsoon time, when the humidity goes up and a few thunderstorms start making their appearance. It was wetter than usual during my time there, which was good for wildlife and waterfall viewing. The monsoon begins in earnest in November, and it rains violently. The floodplains fill, the wildlife mass and nest, it is a time of abundance. By March the weather quiets down, and the breeding season is in full swing and plants produce copious fruit and seeds.
Mid winter is the time of burning and dormancy.
It is the most comfortable time to travel to the area, but you won't see much. When the rains come in spring, the wildlife returns. I went with Northern Territory Adventure Tours, which is a relatively low-budget affair. 9 of us were crammed into a Toyota Land Cruiser where we bounced on the 4WD roads for 3 days. Our guide was a knowledgeable one with considerable bushcraft and local lore, though he did put on a good macho Crocodile Dundee act.