Green’s Dictionary of Slang

outer n.1

[out v.2 (1)]

1. a knockout punch.

[Aus]Queenslander (Brisbane) 8 May 1013/4: Billy Blink (boxing instructor): Great Scott! That was an outer you gave me.
[UK]Tit-Bits 22 Jan. 309/1: Boxing Instructor (loquitur), Great Scot! that was an ‘outer’ you gave me [OED].
[Aus]Bulletin (Sydney) 21 Jul. 24/2: Present writer [...] has seen a great number of ‘knocks-out,’ and is certain that 50 per cent. of them were absolute flukes [...]. Extreme nicety is required to get home a real ‘outer’ on a man dodging all over a 24-foot ring; and, anyhow, the knock-out is not boxing – it is a premeditated attempt to kill!

2. a prize-fighter.

R. Free Seven Years Hard 122: Perhaps the reader may not be aware that [...] a ‘aüter’ [is] a prize-fighter.