We can't rely on the US to bail us out of trouble all the time.
They could be fighting 3 or 4 wars or conflicts at the same time. We have to help ourselves. Timor showed we can't rely on the US for everything, but instead be greatful for any additional assistance that makes it here.
With our new capabilities (and a 4th AWD) we will be able to back ourselves for nearly any regional situation. Other nations can join us, but we are essentially the taskforce.
This is a good thing, because other nations are more likely to join if there is a strong nucleus. So not only are we more capable, but we are more likely to get other countries to follow us.
I can see closer defence links with Malaysia and Singapore because of this. The will look at forming closer ties with Australia directly and not rely, always on the USA.
Australia will become the regional defence hub. Everyone will want to plug into. We will be the ally people want on their side, helping ensure their security. From defence ties flow trade ties, well maybe...
This will allow the US to focus on upcomming threats like a resurfacing russia, a booming china and a whole lot of smaller states that are causing all sorts of grief. As big and mighty as the US is, they aren't the world police. They just aren't that big to control everything, yet.