In A Dictionary of Austral English, 1898, yabber is defined as:

Yabber, n. Used for the talk of the aborigines. Some think it is the English word jabber, with the first letter pronounced as in German; but it is pronounced by the aborigines yabba, without a final rYa is an aboriginal stem, meaning to speak. In the Kabi dialect, yaman is to speak: in the Wiradhuri, yarra.

1888, Rolf Boldrewoo, 'Robbery under Arms', p.55: "Is it French or Queensland's blacks' yabber? Blest if I can understand a word of it".

And so it was initially.  Now, of course, in one of the many contributions of the many Aboriginal languages to Australian English, yabber has in fact completely displaced jabber.  Australians never use the word.  It no longer refers to talk of the aborigines, but rather idle or inconsequential talk generally.  Most Australians would not know that the word was of aboriginal origin. 

For example, "We were just yabbering away when the phone rang".  "He was just yabbering away about something or another".

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