Wikipedia suggests the English name of the concept is imprecise and provides no evidence of a relationship with dreaming:
The term is based on a rendition of the indigenous (Arandic) word alcheringa, used by the Aranda (Arunta, Arrernte) people of Central Australia, although it appears that it is based on a misunderstanding or mistranslation. William Stanner remarked: "why the blackfellow thinks of 'dreaming' as the nearest equivalent in English is a puzzle". It has been argued that the word's meaning is closer to "eternal, uncreated."
Dreamtime. (2017, August 28). In Wikipedia, The Free Encyclopedia. Retrieved 08:40, August 31, 2017, from https://en.wikipedia.org/w/index.php?title=Dreamtime&oldid=797624857
Do dreams play as significant a role in Dreamtime stories as the term suggests?