Sister Australia is a minor character and is one of Denmark's regular hook-ups. The two of them got together in this comic, which is also her only "on-screen" appearance to date, but as indicated here, they are still an item, one which Denmark seems quite proud of. In her relationship with Denmark, she represents Princess Mary, the Australian woman who married Crown Prince Frederik, and by extension the Danish royal family as a whole. So far everything we can deduce about her personality is only from a single comic. Her normal mode of dress is similar enough to Australia's that we can probably assume her basic personality is much like his (for example, her trousers indicate that she is an outdoorsy type, like her brother). However she has a girly side and in her only appearance she wants to be treated like a princess. She is easily charmed by gestures of chivalry and sexually liberated enough to sleep with someone after only one date, if they impress her enough. Sister Australia's top is quite revealing, although she may only be wearing her top in this way because her home country is very hot.
As Australia's sister, Sister Australia is England's daughter as well as a sibling to America, Canada, New Zealand, and Sealand. She also has some unspecified relationship with the rest of the British Isles (Scotland, Wales, and Ireland).