Well, that is the opposite what I have done.
I found the hosts here in Australia charging a lot for less, service poor and downtimes on the high site.
For that reason I am now hosted by an outfit in the UK with their servers in Dallas TX USA
There is ample of speed from Australia to those servers for anyone in Austrlia who wishes to visit the site and I would argue that the speed advantage from Europe to the USA is superior than the speed from Europe to Australia, whish is at time really slow.
So, for people in Australia to view your site in the USofA is not a problem.
Your problem would be more expensive in Australia and maybe slower to update.
About unlimited hosting / bandwidth:
Why Unlimited or Unmetered hosting packages are not possible? - Page 1
My host is now Rochen.com, my experience see:
Thanks to Rochen.com : Sengers’ Blog