That is definitely a kirin, or as we say in Chinese, a qilin (麒麟 qílín pron. chee-leen). It speaks well of Bubbles that a qilin appears in her mind-realm. Qilin will only appear in an area which is controlled by a just, wise, and benevolent ruler, and are closely linked with sages and other wise people.
The colour of dragons has meaning in East Asian mythology. Red dragons are associated with luck, fire, passion and the heart. It is the dragon of summer and the South. Certainly appropriate for our Georgia Peach. White dragons are associated with the principle of yang; positive, active and powerful, as Hanners feels herself to be. White also symbolises purity, which is also appropriate, and mourning, which we hope is not.
I don't know how far Jeph researched this, but he got it pretty much spot on.