An alien was found on a barren planet by a space expedition, they catch it and bring it to earth. The alien did not live on that planet, it was just passing through. The alien was named "Cutie-Pie" by the media because it was beautiful. Later, the alien falls sick because the scientists are unable to determine its natural diet. Then, it escapes, has some adventures, befriends a human baby and later leaves earth. But, there is a telepathic link between the baby and the alien; and it remains for ever.
It was a short story from a collection. Can anyone find out who wrote it? And which publication it appeared?