Thanks. I thought it was just some “design element.”
Because there is also no star (at least no visible star) at the celestial south pole, the Southern Cross is important to using the stars for traditional navigation in the Southern Hemisphere - it's long axis points almost directly at the south celestial pole. That makes it extremely symbolic in terms of showing something is in the southern half of the world.
The large star (directly under the Union Jack) is not part of a constellation - it's the Commonwealth Star. It has seven points - one for every one of the six states, and one that represents the territories combined. In that way, it serves a somewhat similar symbolic purpose to the fifty stars on the flag of the United States - if Australia ever gets another state, a point would be added to the star (the Northern Territory may one day become a state, and there is also provision in the Australian constitution for New Zealand to become a state - at the time the constitution was written, it was not clear which of the Australasian colonies would want to become part of Australia and so it was written so all could: "The States" shall mean such of the colonies of New South Wales, New Zealand, Queensland, Tasmania, Victoria, Western Australia, and South Australia, including the northern territory of South Australia, as for the time being are parts of the Commonwealth, and such colonies or territories as may be admitted into or established by the Commonwealth as States; and each of such parts of the Commonwealth shall be called "a State".