。
She really wants to live in Australia.
Literal
She [topic-は] eagerly Australia [in-で] live-want-to is.
Built on the same third-person desire pattern as countless 'wants to' sentences in Japanese: ~たがる ('appears to want to') is the grammar Japanese uses to describe other people's wants, since direct mental access is reserved for the speaker. The polite past ています shifts up the register slightly. しきりに ('eagerly, repeatedly, intently') intensifies the wanting from a passing wish into something the speaker has noticed her bringing up over and over. オーストラリア is the standard katakana rendering of Australia; the で marks the place where she'd live, since 暮らす ('to live, get by') takes で for the location of one's life — distinct from に, which marks where one resides as a fixed point.