Hosting your application "in the cloud" may require some alteration of your code, depending on the service that you choose. This is a moot point of course if your site is completely static server-side.
You've not stated how much dynamic and static output there is in your traffic pattern - you may get the gain you are looking for without moving the application code by hosting your images and other static content elsewhere, perhaps a shared host or VPS in another country or a "content delivery network" service like Amazon's "Cloud Front" (there are several decent CDNs around, some catering for small users and some optimised for larger concerns which may therefore be too expensive for your scale, so shop around).
20Gb does not sound like a lot of bandwidth (caveat: I know little of the Australian market) so. Am I right in guessing that you are using a "shared hosting" provider? If so then consider a VPS - most (even the cheaper options) come with at least a couple of hundred Mb of bandwidth allowance, some with a full Tb or more (though be careful: many hosts look "to good to be true" value wise and the usually turn out to be!).
If bandwidth is as expensive in your home country than you may have to look further afield even for the VPS option. If your audience is international than this may be a bonus: more of your visitors will get a better response than will get a slower one, but if your core audience in more local to you then you'll have to consider that the site will be less responsive for them if hosted on the other side of the trans-pacific links. This will be an issue for you no matter what hosting options you use (shared, VPS, "cloud", ...).