Roo

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early 20th century: shortened form.

wiktionary

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From Middle English roo, ro, from Old English rō, rōw(“quietness, quiet, rest”), from Proto-Germanic *rōwō(“quiet, rest”), from Proto-Indo-European *ere(w)-, *rē(w)-(“quiet”). Cognate with Scots ro, ruve(“peace, repose”), German Ruhe(“rest, peace, tranquility”), Danish, Norwegian and Swedish ro(“rest, peace, tranquility”), Icelandic ró(“tranquility, quietness”).

Aphetic form of  kangaroo. 

etymonline

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roo (n.)

Australian colloquial shortening of kangaroo, attested from 1904.