The three characters read 임(Im)다(Da)미(Mi). This is her Korean name.
I feel ダミ･イム and イム･ダミ are both fine. But, I prefer ダミ･イム.
Basically, we try to copy native pronunciation of that person. For example, Michael has several ways of reading in Hebrew, English, German, French, etc. So, it is written in various forms like ミカエル, マイケル, ミハエル, ミチェル, etc. It seems that Dami Im is mainly based in Australia, and she is now an Australian. So, I want to import her name from English.
Probably, Im is 任 or 林, but basically there is no way to know what Kanjis are appropriate unless you ask her parents or herself. Now Koreans do not use Kanji in their daily life although most Koreans have their Kanji name. If you go to her wedding, probably you will see her Kanji name.
You can find several Kanji examples of 임다미 in the link below. 林多彌, 林爹彌, 林茶彌, 任茶迷, 林爹媺.
In old days, Japanese tend to write Chinese and Korean name in Kanji, and read it in Japanese way. For example, Kim Dae-jung (金大中), a president of South Korea, was called きんだいちゅう (Kin DaiTyuu).
However, there was a movement to read Korean names in a native way (現地読み) in 1984. Korean government had asked Japanese government and media to do so. And, Japanese government accepted this just before a president, Chun Doo-hwan (全斗煥, チョン・ドファン (Korean reading) or ぜんとかん(Japanese reading)) came to Japan. Japanese media also followed.
As a result, we tend to read 金大中 as きむでじゅん (Kimu DeJun). Still, the old way of reading is OK.
On the other hand, Chinese government reads Japanese name in Chinese way, and they have not asked this.
So, nothing has changed for Chinese names. (For example, Hu Jintao, 胡錦濤 is こきんとう Ko KinTou. Yet, フーチンタオ is OK, but it is hard to understand this.)
The reason why we tend to write a Korean politician or scientist's name in Kanji is probably that s/he is so old and famous that we know their Kanji name. It is shorter and easier to understand.
But, as for young singers, we do not know their Kanji name anyway.