Doreen is sister to Masa & Mune, a dream creature possibly created by Melchior (as he created her siblings). She spends her time in Enhasa and has philosophical leanings; she questions Crono's party concerning reality. She serves no other purpose in the game.
"Am I a butterfly dreaming I'm a man... Or a bowling ball dreaming I'm a plate of sashimi? Never assume that what you see and feel is real!" is a reference to the philosopher Zhuangzi, a Taoist who wrote the Tao Te Ching. According to legend, after he arose from his sleep he proclaimed he had a most vivid dream. He dreamed that he was a butterfly and all his experiences he perceived to be utterly real. He then stated (more or less), "Am I man dreaming that I was a butterfly or am I a butterfly dreaming that I am a man?" The famous passage helped relate many of the metaphysical principles of eastern and even western religion. Woolsey created this reference, as the Japanese originally featured Doreen getting right to the point about perspectives differing among people.
It is possible that Cross suggests Doreen corresponds as a "dream of Melchior" to the pendant as Masa and Mune do to the Masamune, since Doreen appears by Kid's side after the orphanage episode passes (and she's holding the pendant).