When and if they try to penetrate your existing market, or to register their trademark in the USA, you MIGHT have a claim against them. Until then, all you have is a "locally known" business name, although you seem to suggest you are using the business name as a trademark or service mark.
Under US (and Australian) laws, the first to use a distinctive brand in commerce on particular goods or services has "priority" over anyone who comes later and starts using or tries to register a "confusingly similar" brand.
OTOH, a domain name is not a trademark, nor is it a business name. A domain name is a globally unique internet address identifier. Trademarks and trade names are "local" unless you have registrations that pioneer new frontiers for your offerings.
As mentioned, if they have swiped your creative works of original authorship in the imagery of your logo, that could be a copyright infringement, or at least the basis for contacting them about your superior rights. Unfortunately, within seconds, they could go ahead and file an application for registration of their brand in the USPTO, giving them a "leg up" on USA rights, other than where you are "actually doing business" under that brand.
So, looks like you may need to buy yourself some happiness by filing an application for a US trademark registration. It's $325 well spent on at least one class of goods or services, thus putting your brand into the official international record.
Come on back if you need more ideas about where to go for more information.
http://www.uspto.gov/trademarks